Sorry for the delay:
Here is THE LIST, or at least as I have it in my notes.
Required anime:
Serial Experiments Lain
Trigun
FullMetal Alchemist
Ghost in the Shell
Sailor Moon
Macross
Gunbuster
Azumanga Daioh
Slayers
Tenchi Muyo!
Gundam/Gundam Wing
Vampire Hunter D
Cowboy Bebop
DBZ
Lupin
Pokemon
Revolutionary Girl Utena
La Blue Girl
Rurouni Kenshin
Akira
Fruits Basket
Escaflowne
Kodomo no Omocha (Childs Toy)
Fushigi Yuugi
Neon Genesis Evangelion
Some creators whose general catalogue is important enough that you should be familiar with their names, as well as their key works:
Leiji Matsumoto
Rumiko Takahashi
CLAMP
Hayao Miyazaki
Osamu Tezuka
Fans should also know of Studio Ghibli and Studio GAINAX.
We gave an honorary shoutout to FLCL and Naruto as well.
To elaborate on the lists above:
Serial Experiments Lain - There was a period of time where everyone had seen this anime, and it has survived as a part of the identity of modern fandom to this day. It's mix of surealism and darkness with abstract story telling and a definite plot which was just out of reach came at a good time in American fandom, when many of the Sailor Moon Boom were ready to move past the kiddy stuff but didn't have a good directon to follow. The unique art style drew many in, and the product as a whole pulled many of us into the darker, more bizzare side of anime.
Trigun - Another series that served as a gateway to more complex story lines and the more mature side of anime. While Trigun isn't as deep or as well made as many other anime, it did bring up a lot of adult concepts and probing questions that were foreign to most anime fans. It also has spanned two generations of fans, by being immensly popular when it was first released, as well as having a second wave of popularity following it being aired of Cartoon Network.
FullMetal Alchemist - This show has done a lot to bring older and younger sects of fandom back together. While a lot of newer fans tend to live in the realm of gimmics, gags, and mindless moe, FMA was able to draw them in with its light humor, cute character designs, and silly gags while still delivering an incredibly well written storyline with a lot of dark, gritty elements that rival even some of the stuff from the late 80's. Between the compelling characters, the rich storyline, and the deeply emotional scenes it has become a show that all anime fans can (and possibly should) identify with.
Ghost in the Shell - The movie was much like Akira, in that it was something that many MANY people saw, and did a lot to shame America's mental image of anime. It remained a classic in the anime community, and any chance it would have had to drop in notability was destroyed with release of Stand Alone Complex, which many older fanboys consider to be the best made anime series, possibly ever. Combining kick-ass action with hardcore intellectualism, it's a show that a lot of fans can get behind.
Sailor Moon - This was the gateway anime to end all gateway animes. This show managed to bring in thousands of fans, in multiple waves (from when it was on air, and later when it was on Cartoon Network). While it is objectively terrible, it is an anime that nearly everyone who has been a fan for more than 5 years has seen.
Macross - One of the few anime to be as important here as it was in Japan. Macross also served as a major gateway to anime fandom. Under the title "Robotech", Macross brought in three distinct waves of fanboys, and unlike Sailor Moon, it has held up as an important series that fans today excitedly show their friends. One of it's many sequels, Macross Plus should also recieve an honerable mention. For about four years after Macross Plus came out, if you were a fanboy and you had not seen it you were likely to be mocked and shamed.
Gunbuster - This is one of the anime that history (and older fanboys) will not allow you to forget! The first GAINAX super robot anime, Gunbuster somehow epitomized the genre while somehow parodying it. With mindblowing action, unfathomable scale, and heartrenching scenes that have made even the most manly and hardcore fanboys cry, Gunbuster is an absolute work of art, and should be respected as such. Recently rereleased in tandom with its 25-year later sequel Diebuster, it is currently being shown to a whole new generation of fans.
Azumanga Daioh - A much more gentle and nostolgic show, it fills a void left by most other anime. While the slice of life genre of anime is gaining popularity (largely due to Azumanga), none have yet captured the mature vantagepoint that Azumanga Daioh maintained. It is a show that younger fans can enjoy at face value, and older fans can enjoy and respect as a look back on their own days in High School.
Slayers - Slayers is terrible, but for a long time it was a heavyweight in fandom. While you may not ever have to watch an episode of Slayers, it is certainly useful to be familiar with it as a whole. Honestly, every fan probably should sit down with a tape or two of it.
Tenchi Muyo! - This show was outrageously popular, appealing to both the fangirls love of awkward situations and silly gimmics, and the fanboys love of big bouncy breasts! Combining hardcore sci-fi with a love triangle soap opera, Tenchi was able to hold the attention of men and women alike, and as such became a staple of fandom. Though the later serieses were not as good, it remained a dynasty in fandom, and has recently seen some new material being released. It was also picked up by Cartoon Network, thus cementing it as a part of our collective cultural literacy.
Gundam/Gundam Wing - The Mobile Suit Gundam franchise needs no explanation. It is impossible to go to a convention and not find a hardcore, old school fan of Gundam. If you are a war-nut, into mecha, or just a man you will eventually find the original, and it will never leave the backdrop of fandom. General fans though tend to have an idea about Mobile Suit Gundam, but not a clear one. They do however almost always have exposure to the Gundam Franchise. Be it Gundam Wing, Gundam Seed, or even G-fighter, almost every anime fan has watched (and enjoyed) a Gundam saga, and many have seen seven or eight of them.
Vampire Hunter D - Another movie well known outside the anime community. By subject matter alone D found a huge fanbase in anime fandom, and when paired with a good animation budget, and art by Amano, it was a guarenteed hit. It is also notable for being first released in English worldwide before it was in Japanese.
Cowboy Bebop - Action, depth, and dark story telling stripped of most moral fiber and emotional substance, Cowboy Bebop holds a great appeal to disenfranchised youth and adults alike. Like Trigun, it had a 1998 release that was very well recieved, followed much later by a Cartoon Network airing that refueled its popularity and kept it fresh in the American mind.
DBZ - Say what you will, if you don't know who Vegeta is you are not an anime fan.
Lupin - One of the most classic and beloved characters in Japan, Lupin was much less known in America. Although it was released several different times here, it has never been a smash hit. However, any fan worth his salt has heard of it, and knows of the significance. Said fans are also aware of the many MANY cameos and parodies that spring up in other anime. Recently Lupin was given a top-notch dub and thrown onto Cartoon Network, finally finding a general fanbase to augment its already notable place in the hearts and minds of the more seasoned fans.
Pokemon - Same as DBZ. If you don't remember the episode where Ash gives away Butterfree then where were you? Much like the old axiom "If you remember the 60's then you weren't there", if you didn't catch 'em all then you weren't an anime fan.
Revolutionary Girl Utena - Although it is waning in popularity, its notory keeps its place in fandom alive. Sometimes known for being "That lesbian show", its subject matter tends to bring curious fans in. Its unique style of story-telling, abstract direction, amazing music, and out-there visuals hold the audience and inspire them to share it with their friends.
La Blue Girl - Possibly not notible in its own right, but rather as "the hentai everyone has heard of". Even though many fans have never actually seen any real hentai (or at least an entire episode of it), hentai holds this sacred place in american fandom, perhaps as a collective "how do you like this?!" to our cartoon patriarchs. If asked to name a hentai, 9 out of 10 anime fans will probably say "La blue girl", though Bible Black gives it a run for its money.
Rurouni Kenshin - One of those shows that everyone saw. If you didn't request the fansubs for months and months and months, then you probably bought the VHS release for years and years, watched it on real player digi-sub releases, or finally caught it on Cartoon Network. It has a huge fanbase, but a much larger subsect of fandom has seen ALL of it, then never looked back. Regardless though, most fans will know what you are talking about when you mention it.
Akira - That which earned anime the respect in the American film community that it honestly doesn't deserve. Visually stunning, bloody, confusing, and generally out-there, Akira set the stage for many pretentious film and theater buffs to make the jump over to anime fandom. It also gave us something to show our parents/friends when they made fun of us for still watching cartoons, back before anime was more mainstream.
Fruits Basket - Hyper popular amung fangirls and younger fans, this show combines over the top gag humor with angsty and confusing love triangles. Although rarely seen by fanboys, it is "required reading" as almost any anime fan knows who Kyo or Tohru are.
Escaflowne - By combining mecha, shojo, and Yoko Kanno Escaflowne had something for everyone. Its TV appearance helped build its fanbase.
Kodomo no Omocha (Childs Toy) - Possibly the most watched fansub. Back when Shojo was king, "Kodocha" was princess. Hyper slap-stick meets emotions. With a recent (and LONG awaited) domestic release of the series, and with the manga selling well, it looks as though Babbits will be a part of American fandom for some time to come.
Fushigi Yuugi - A lot of people watched this show. It was a commoner at anime clubs back when clubs WERE the anime scene.
Neon Genesis Evangelion - That which destroyed Super Robots forever. GAINAX's second super robot show. Dark, psychological, depressing, depressed, and possibly religious. Whether you llove it or hate it, Eva is one of those shows that fans can debate over for days straight. Many fans have never moved past it. Be it a post-modern masterpiece, or the angry penstrokes of a desperate animator amidst a nervious breakdown, Eva will not be forgotten.
Leiji Matsumoto - Originally a shojo comics artist from the 70's, Matsumoto carved out his place by releasing space epic after space epic. Famous for Yamato (Star Blazers), Harlock, and Galaxy Express, he has pumped out classic after classic, almost always set in the same basic (often conflicting) universe known to fans as "The Leiji-verse". Although his plots are independent, the characters tend to cross with each other thoughout the works, and almost all of his stuff is thematically the same. He has also had serveral notable works outside of the Leiji-verse including the WWII "what-if" anthology "The Cockpit", and "Interstella 5555", the animated movie version of Daft Punks "Discovery" album.
Rumiko Takahashi - Creator of Urusei Yatsura, Maison Ikkoku, Ranma 1/2, and Inu Yasha, she specializes in bland stories that have no intention of ever ending. Despite the formulaicness of it all, her stuff his generally well regarded, and each of the serieses listed above are worth knowing well.
CLAMP - An all woman team of manga-ka, CLAMP has written many fan favorites, including X, Magic Knights Rayearth, Angelic Layer, Chobits, and Card Captor Saskura.
Hayao Miyazaki - Co-founder of studio Ghibli, this man has directed most of the anime that your mom has seen. Castle in the Sky, Princess Mononoke, Nausicaa, Porco Rosso, Kiki's Delivery Service, Spirited Away, and Howels Moving Castle are all his.
Osamu Tezuka - The "God of Manga", and "Father of Anime", Tezuka has had a prolific run, writing countless stories, and producing some of the very first anime, as well as some of the most ground breaking. Though few of his titles are well known today (though many know of Astro Boy, Metropolis, Black Jack, Unico, Kimba, and Phoenix), he is someone who should be known and respected.
Thanks Mike, wow I didn't expect such a detailed response!, so no worries about the delay.
Hmm sure am glad that I have seen most of whats listed, although it looks like I'll have to start working on some of them. Thank god for summer ^_^