By 1980, WSJ still held its classic model for what was considered shonen, but times were starting to change.  Series such as “Kinnikuman” and “Ring ni Kakero” were starting to give them an edge in shonen action and KochiKame was already established for its day-to-day comedic style.  However, it was at the start of this year that a young mangaka named Akira Toriyama came around with his first new series: “Dr. Slump”.  With his arrival, WSJ began its journey towards its modern form as action and comedy both became more defined and giving the magazine an edge over its rivals.  The push created by Yumetamago and Kurumada were eventually solidified with the arrival of Tsukasa Hojo and his sexy ladies of action and Yoshihiro Takahashi creating a dog-fighting-bear tales, but pushed to a completely new level when Buronson joined with newcomer artist Tetsuo Hara to create a classic post-apocalyptic action epic.  Sports seemed to take a back seat in this era, but it wasn't enough to stop Yoichi Takahashi from attempting to bring blood to soccer to the country.  And while Toriyama and Akimoto were already establishing themselves in the comedic realm, mangaka such as Motoei Shinzawa, Izumi Matsumoto, Tokuhiro Masaya and a young Masakazu Katsura were all taking different approaches for using comedy and their own approach to modern school kids.  By the end of this period, Jump had become known for both its comedy and action with other young talent such as Hirohiko Araki starting to cause ripples, yet with the end of Dr. Slump by the end of this period, Toriyama was only preparing himself to release an even bigger story from his weird world: a tale about a boy with a monkey tale and the massive action and adventure he would face.

-Dr. Slump
-Mangaka: Akira Toriyama
-Run: 1980-1984
-Anime: 1981-1986, 1997-1999
-Producer: Toei, Fuji TV

All Senbei Norimaki wanted with his latest creation was a daughter...but what he got was a powerful, childish, nearsighted robot girl who just never seemed to stop getting herself into things!  From time travel to alien invaders to fighting the other insane mad scientist in Penguin Village, no one's life was ever the same once they met Arale!  A comedic legend from the moment of its first publishing, "Dr. Slump" immediately put Toriyama on the map of the young mangaka of the era, displaying his own wit and satire and using his comedic talents to become the premiere writer of the era.  The popularity of the series, however, was completely global as it aired within Europe and Latin America, usually alongside Toriyama's "other work".  Ncha!

Opening: http://www.youtube.com/watch?v=OLiku1IcPnM

-High School! Kimengumi
-Mangaka: Motoei Shinzawa
-Run: 1980-1987
-Anime: 1985-1987
-Producer: Studio Comet, NAS, Fuji TV

School: one of those places where you meet people of all sorts of personalities, all sorts of traits...all sorts of dysfunctions.  And when a bunch of weirdoes get together, particularly if their names end up leading to some sort of weird Japanese pun...then you probably know you are in trouble and your life may never be the same!  Originally known as "Sannen Kimengumi" when starting (the anime stuck with the longer-living name), Shinzawa created one of the more memorable comedy series of the 80s hanging up there with the wild action and adventure series in the magazine.  Of peculiar note: Kimengumi was one of the key anime that turned France on to the anime world!

Opening: http://www.youtube.com/watch?v=95freerrfSM

-Captain Tsubasa
-Mangaka: Yoichi Takahashi
-Run: 1981-1988, 1994-1997
-Anime: 1983-1986, 1989-1990, 1994-1995
-Producers: Tsuchida Productions, TV-Tokyo (original), CBS-Sony Group, Movic (Shin), NAS, Fuji TV (J)

For Tsubasa Ozora, the game of soccer (or football in most of the world) came easy to him, but his life traveling with his parents made it hard for him to hone his skills.  However, after gaining guidance from good friends and a Brazillian master of the game, he begins his journey, from elementary school to the pros, to bring his ultimate dream into reality: a World Cup championship for Japan!  Initially run in the early 1980s with his early years, Yoichi Takahashi kept coming back to the series that brought him fame time and time again, first with his "World Youth" manga in Jump in the mid-1990s, then moving Tsubasa's later years to older magazine Weekly Young Jump where his saga continued.  The anime rendition of Tsubasa's journey penetrated across the world to all the soccer-mad people, including Brazil itself!

Edit: Captain Tsubasa is one of the most influencial sports manga/anime around the world, to the point that Takahashi even received an award by FIFA! There is a popular "urban legend" concerning the ending of Captain Tsubasa, but it is obviously fake since Captain Tsubasa hasn´t "finished" (added at the suggestion of perrolococz)  Furthermore, various famed international soccer stars are also admitted Tsubasa fans. (suggested by khursten)


While four seperate animated renditions were created of Captain Tsubasa, the first three were the only ones to concentrate on the WSJ era, with only the last (Road to 2002) from the Young Jump era.  The original Captain Tsubasa covered the early parts of the story, the OVA "Shin Captain Tsubasa" journied to the end of the first series, and "Captain Tsubasa J" came out at the same time as the "World Youth" manga...and just in time for the 1994 World Cup in the US.
Original Opening: http://www.youtube.com/watch?v=n9dPJsrPhLI
Shin Captain Tsubasa Opening: http://www.youtube.com/watch?v=AenybtdjrYM
Captain Tsubasa J Opening: http://www.youtube.com/watch?v=lGA4pxs9boQ

-Cat’s Eye
-Mangaka: Tsukasa Hojo
-Run: 1981-1985
-Anime: 1983-1985
-Producers: TMS, NTV

By day, the Kisugi sisters are just normal girls, running their cafe and going about their lives.  But by night, the girls partake a startling change of profession, turning into a trio of art theives notorious as well as extremely sexy!  But of course its all in the name of charity...not to mention finding their dad who originally got them in the first place.  A classic in both manga and animated rendition in Japan and certain parts of Europe, this was the series that brough the urbane and deadly Tsukasa Hojo into the shonen ranks, yet had him playing with the girls in more way than one!

There were two seperate "Cat's Eye" anime, but this is only from the first...mostly due to the infamy of the second going nowhere with Hojo's plot.
Opening: http://www.youtube.com/watch?v=Y955Kek_alM

-Stop!! Hibari-kun!
-Mangaka: Hisashi Eguchi
-Run: 1981-1983
-Anime: 1983-1984
-Producers: Toei, Fuji TV

His name was Ibari Ozora, the son of a mafia leader.  But when he found himself under attack by a rival gang he chose to lay underground...becoming Hibari, a rising female idol!  OK, I really don't know this series that well either but basically this is one of those "men who become women" manga series and was the only anime created from the weird and prolific works of Hisashi Eguchi (more known in Japan for his earlier baseball series "Susume! Pirates")  But trust me: this just feels so much like that Kinks song "Lola"...yeah. (well it explains the "Stop" in the title, I think)

Opening: http://www.youtube.com/watch?v=1tVA1QlPk-o

-Fuma no Kojiro
-Mangaka: Masami Kurumada
-Run: 1982-1983
-Anime: OVA (1989-1992)
-Producers: Toei

In a modern Japan with ninjas running amuck, Kojiro is the heir to the legendary Fuuma family.  But with other ninja running amuck, its going to be one of those things he's going to have to fight with.  The first series created by Kurumada after "Ring ni Kakero"'s ending (but before something else), the series is a minor yet slightly know one in Japan.

While three OVAs were made, no animated OP could be found anywhere, just the opening to a recent live-action version.  So sadly, this remains blank.

-Yoroshiku Mechadoc
-Mangaka: Ryuji Tsugihara
-Run: 1982-1985
-Anime: 1984-1985
-Producers: Tatsunoko Productions, Fuji TV

Its sort of weird to say this but in a world where Initial D is massive, its surprising to see WSJ actually have a series based on automobile racing and maintenance.  Based around the maintenance shop "Mechadoc" (short for "Mechanical Doctor"), this series mostly is based around taking care of cars, tuning them and racing them against the best around.  Although a slight hit in Japan, this series surprisingly was also known in Italy...but that's the land of the Ferrari!

Opening: http://www.youtube.com/watch?v=1UrCoUgf6BM

-Wingman
-Mangaka: Masakazu Katsura
-Run: 1983-1985
-Anime: 1984-1985
-Producers: Toei, TV Asahi

Once upon a time, a being from another realm dropped a magic notebook into the hands of a male student, who subsequently used the notebook's power to change the world.  Now, before you go blurting out what you think I'm talking about, realize this: its 1983, its called the "Dream Note", its been dropped by a cute female, and the notebook doesn't kill anyone...just allows the writer to have any of his wishes come to reality, including, as our hero does, becoming a hero of justice!  So with that out of the way...this was the series that brought mangaka Masakazu Katsura early manga success, bringing his love of heroes and cute girls out there and proving sometimes you do need a hero in this chaotic era, particularly in a world with cute girls.

Opening: http://www.youtube.com/watch?v=T85IqlZYbYQ

-Hokuto no Ken (Fist of the North Star)
-Mangaka: Buronson/Tetsuo Hara
-Run: 1983-1988
-Anime: 1984-1987, 1987-1988 (later OVAs in 2003-2004, followed by other movies/OVAs made in 2006-2008)
-Producers: Toei, Fuji TV

The year is 199X.  The world has collapsed into anarchy in a post-apocalyptic society.  Gangs run amuck through the land and evil tyrants control the people.  From out of this cesspool of chaos comes a warrior: trained in the deadly art of Hokuto Shinken, he uses fists and pressure points to literally make his enemies explode...not to mention make his shirts explode when going into battle!  But Kenshiro has his own reasons for fighting in this wasteland: revenge and justice!  One of the series that defined WSJ of the 1980s and the hyper-action manga of the era, "Hokuto no Ken" (or its more well known name: Fist of the North Star) remains a testament of action series in Japan and the world over.  In particular, a Streamline release of one of the movies was one of the early defining anime moments in the United States! (even if we still don't quite get who won that final battle)

Two seperate anime were created from the original FoNS source (not counting remakes): the original anime covered from the beginning of Kenshiro's journey through the end of the original storyline with the battle against his "brother" Raoh.  The second anime, "Hokuto no Ken 2", takes place after a timeskip...particularly so the brats that Kenshiro was guarding could probably have more to do.
Original Opening: http://www.youtube.com/watch?v=n371zCCYpts
Hokuto no Ken 2 Opening: http://www.youtube.com/watch?v=bhF-bKMT5rc

-Ginga -Nagareboshi Gin-
-Mangaka: Yoshihiro Takahashi
-Run: 1983-1987
-Anime: 1986
-Producers: Toei, TV-Asahi

It just seems too bizarre of a concept if you hear it up front: a dog (Akita Inu is the breed) runs away from home and joins up with a pack of wild strays, gathering together an army to fight against an evil monster bear that is terrorizing everyone on two legs and four in the mountains.  However, mangaka Yoshihiro Takahashi (a formerly established mangaka in WSJ) made the story his own after hearing a story in the news about stray packs, creating a powerful tale of heroism, courage and...well, canine/ursine warfare.  While popular in Japan, the series made its biggest mark in Scandinavia as their own anime classic! (then again it is a lot of snow and mountains)

Opening: http://www.youtube.com/watch?v=av26bdxfnr8

-Kimagure Orange Road
-Mangaka: Izumi Matsumoto
-Run: 1984-1986
-Anime: 1987-1988, 1989
-Producers: Studio Pierrot, Nippon TV

It may seem like a typical boy-meets-girl sort of story, but with a weird twist here or there.  Kyosuke Kasuga is a teen in a family of psychics, arriving in a new town where he discovers a mysterious beauty in a red hat.  However, this beauty, Madoka Ayukawa, isn't the girl he thought she was on first sight.  And making matters worse is how Madoka's friend, Hikaru Hiyama, discovers Kyosuke's secret and falls for him!  A classic love-triangle manga/anime series, Kimagure Orange Road gained noteriety both in Japan and within fancircles in the US before its eventual release in recent times (well the anime, the manga is still unreleased in the US). 

Opening: http://www.youtube.com/watch?v=v5sTn7HMTpQ

-BAOH: The Visitor
-Mangaka: Hirohiko Araki
-Run: 1984-1985
-Anime: OVA (1989)
-Producer: Studio Pierrot

An evil organization implanted a parasite known as BAOH into the brain of an innocent man.  The parasite allows him to transform into a powerful immortal beast with many superhuman abilities.  But he had other ideas: breaking out and taking a young psychic with him, the duo are now on the run from the people who want them both for their own schemes.  Although a short two-volume horror-action series, BAOH started to give reputation to a young mangaka named Hirohiko Araki, prior to him starting "something bizarre" in the years to come.

There really isn't much of an opening so I included the ending for this as well...then again there's none of the graphic weird stuff in the ending either.  Maybe you probably can look at one of the AMVs for it instead, I don't know:
Opening: http://www.youtube.com/watch?v=6BqkUsq6g08
Ending: http://www.youtube.com/watch?v=uOOL420wbCA

-Dragon Ball
-Mangaka: Akira Toriyama
-Run: 1984-1995
-Anime: 1986-1989, 1989-1996
-Producer: Toei, Fuji TV

In a world unlike our own, there exists seven mysterious crystals known as "Dragon Balls".  Anyone who is able to collect the seven Dragon Balls will gain the ability to summon Shen-Lon, the Eternal Dragon, in order to make one wish of anything in your heart's desire.  While he didn't know of the legend, a young monkey-like boy named Son Goku did possess one of the balls, a memory of his late dead grandfather who raised him and taught him martial arts for survival. (and whom he unknowingly had a hand in accidentally killing)  One day, a genius girl named Bulma arrived to retrieve Goku's ball and in need of a bodyguard, of which the monkey boy decided to come along.  And thus begins the legend of what many consider one of the most popular manga/anime series of all time and the one title WSJ is known for the world over.  Originally keeping to the comedic style of "Dr. Slump" with action and adventure thrown in and a loose telling of the classic "Journey to the West", the series slowly evolved into a pure action epic as Goku made friends, fought enemies and slowly discovered the power and the interstellar destiny he held within him.  While many complain of its faults: battles that take too long, not ending after certain points, continued exploitation in a stupid sequel anime series, no one can really deny DB's place in WSJ legend...let alone how it held the whole magazine on its massive shoulders from the mid-80s to the mid-90s.

Due to the changing nature of the series, it was divided into two sections.  The original "Dragon Ball" mostly deals with the fantasy, adventure and comedy aspects of the world as Son Goku establishes his heroics.  In 1989, Toei reclassified the series as "Dragon Ball Z" as the action was ramped up and the battles became more intensive as Goku's lineage and legacy is firmly established.
Original Opening: http://www.youtube.com/watch?v=6YsVBjam5uE
Dragon Ball Z Opening: http://www.youtube.com/watch?v=GG3NXDWm3uE