They were the first U.S. manga publisher who published a lot of unflipped, read-it-right-to-left manga in English.note This had been done before, but extremely seldom. We're talking a total of less than ten manga books, tops, and most of them were too obscure for either comics fans or manga lovers to have heard of them.
The affordable ten-dollar digest editions that pretty much all U.S. manga publishers use nowadays was their idea. Before Tokyopop started publishing those, the norm had been to publish translated manga flipped left-to-right, in single-issue comic books with a chapter or two in each issue, which were then collected in trade paperbacks, just like American comic books.
Another idea of theirs was the concept of having your manga sold in bookstores instead of in comic book stores - which really helped increase their potential customer-base.*
This is also because a lot of bookstores may be placed in area(s) of the town where kids without cars can access them - ie the mall. Not to mention, comic book stores don't even exist in some towns in Flyover Country - but bookstores themselves do.
And content-wise, they were the first ones to publish high school romance shoujo manga. Pretty much all of what little shoujo had been published in the USA up until that point had featured some element of adventure or fantasy that the publishers hoped would appeal to male readers, but Tokyopop published high-school romances like Kare Kano and Marmalade Boy, that had no supernatural or adventure elements and were clearly intended for girls (but good enough to be read by anyone regardless of gender). In short, Tokyopop were the first American manga publisher to fully accept that manga didn't have to pretend to be American comic books. Nowadays every publisher does this, so Tokyopop's editions come off as cheap-looking compared to, say Viz's and Kodansha's manga. Especially the early Tokyopop releases. The translations of Sailor Moon and Magic Knight Rayearth were absolutely painful with spelling and character name inconsistencies galore. And the fact that it's unflipped is just Asbestos-Free Cereal now that it goes without saying that you don't flip your manga.
Cutey Honey will make you cringe, until you realize it created the template for anime fanservice, for the Warrior Magical Girl achetype and possibly featured the first Action Girl main character. If you don't remember it from the early 70s, you'll think it's just another typical high-schooler gone superhero story.
Doki Doki School Hours got hit by this hard. The manga is one of the early examples of the "Wacky Homeroom"-format, up to and including a childish teacher, and likely formed the inspiration for other mangas like Azumanga Daioh and Lucky Star. Alas, the anime got released after those other series, which made a lot of viewers cringe at the "tired and old" jokes.
Dragon Ball for that matter. It seems horribly cliché now (even more so than Fist Of The North Star, if only because it was copied more, or at least more directly) but it was refreshing at the time. One of the big ones is the Idiot Hero, which has been done to death in Shonen, but Goku was one of the first (though predated by the title character of Kinnikuman (and besides that Goku is more naive than stupid. That's The Theme Park Version for you - the real version will take forever to read)).
Fist of the North Star seems like horribly cliché shonen, but keep in mind it more or less helped create many of the shonen tropes that exist today. Along with Dragon Ball, many people cite it as a Gateway Series or an inspiration for other Shonen creations.
Ghost in the Shell. The English dub of the original most likely comes off as Narmy to most modern-day viewers, but in the 90s it was considered a major step forward for anime dubbing, featuring a reasonably faithful translation of the source material, correct pronunciations of Japanese names, and semi-believable voice acting.
Since the standards for anime dub voice acting have improved so much in recent years, many dubs that were considered huge steps forward in quality for their time have become increasingly unpopular among modern viewers. Examples include Ranma ½ and Neon Genesis Evangelion. An even better example would be the Tenchi Muyo! franchise. Back in the day (around 1994, to be exact), the use of union actors combined with clever dub scripts was considered a groundbreaking development in the world of anime dubbing. While many people still look back fondly on the dub even now, more level-headed viewers without a Nostalgia Filter will notice the dubs' miscast actors and actresses, awkward delivery and overall poor acting quality in comparisons to modern dubs for anime like Gurren Lagann and Fullmetal Alchemist.
Hayao Miyazaki. Many of his movies have been copied so extensively by both anime and manga that people complain about them being "cliché". No, Laputa isn't just "another ancient civilization on a floating island", it is THE ancient civilization on a floating island. Ironically enough, even though it was this movie that really started Japan's fascination of highly advanced, extinct ancient civilizations, both the name and the concept of the floating island of Laputa comes from Gullivers Travels, written more than two centuries earlier.
Love Hina. Yes, if you just started reading or watching it today, it just seems like another cliché harem anime. This mainly comes from the fact that the show redefined nearly every rule of modern anime romance/harem comedy, and has been copied relentlessly since.
Magical Girls. If you're not an old-school, die-hard fan, you'll probably think that everything in the genre is a ripoff of Sailor Moon.
Sailor Moon itself gets this as well, as it created a sub-genre, and in many countries also contributed to make Anime popular in the first place. When compared to somemoremodernshows, it can look overly cheesy, Filler-ridden, and low-budget.
Maria-sama Ga Miteru is gradually getting there; the series has been copied and especially parodied mercilessly, to the point where viewers suspect it to be a parody itself. Admittedly, the romantic entanglements between the girls of the depicted all-girl school do get rather fluffy and melodramatic at times, but it mostly kept in check by the tight storytelling and outstanding voice-acting in the anime.
Mazinger Z, the Trope Codifier for Super Robot shows, never got that much love outside of Japan, due to the fact that it was usually picked up sometime after successive shows, such as Voltron and even Grendizer got popular, leading to Mazinger often being called a ripoff of its own derivatives.
Osamu Tezuka falls victim to this in the American market. His characters look much closer to Disney and Fleischer cartoons than modern anime and manga, making his art look quaint to modern manga readers. Additionally, it's hard to spot the sheer innovation in his page layouts and stylized pacing when they've more or less become the norm after around fifty years.
Robotech. With its dramatic tone and unvarnished depictions of the death and destruction caused by war, it was the first localized anime to really display Japanese animation's capacity for weighty, dramatic stories to a western audience. With uncut translations of space opera now a dime a dozen, and with the series' multiple flaws now harder to forgive, many now ignore the series' achievements and instead focus on the compromises made in the franchise's creation—namely, the stitching together of three distinct and unrelated anime series into one narrative, necessary for the series to get a syndication deal. The Macekre page goes into greater detail about the significance of Robotech, despite the title being a Take That to Carl Macek for said compromises.
The Expanded Robotech Universe, particularly Sentinels, blew the marriage of Rick and Lisa out of proportion by modern standards. The wedding took two comic book issues to tell and that was after about ten issues of "anticipation" leading up to the big day. Sentimental fans might be to blame. New fans were wondering when they were going to just launch the mission.
Saint Seiya suffers from this quite badly if one were to watch if after seeing more recent Shōnen series, especially during the Gold Saint arc. It pretty much created the Rescue Arc, and if not, it certainly was what popularized it.
Astro Boy is THE Anime and Manga. It was the first truly popular piece in not only Japan, but also in the States, where it was one of the first Animes we had ever received. It's hard to articulate how much Astro Boy means to the medium; it's on par with MICKEY in how important of an animated work it is.