Ankh-Morpork Guard said:
And I'm surprised how many things people are listing that are really NEWER shows. C'mon people, am I the only person hanging onto the 'past' of Anime here?
...I'm too young to be the Anime Diaglo....
I'll step into the breach.
1) 1986 - The Dirty Pair Movie (AKA Project Eden - A name which does NOT appear on the original Japanese LD). That classic DP destruction, one of the best soundtracks EVER, a terrifically over the top villian and some of the best action sequences ever.
2) 1984 Urusei Yatsura Movie #2 : Beautiful Dreamer - Urusei Yatsura is in my opinion the prototype for the looser boy with magical harem girls shows, only without the treacle.
Ataru (the main character) is the unluckiest guy in the world and an incorrigable letch, actually quite capable in his own way and certainly one of the toughest characters in anime. He's Cursed/Blessed with constantly encountering the galaxy's most beautiful and powerful women, most of whom seem destined to become involved with him usually unwillingly since they all recognize his unsavory character. Given that his "wife"/Girlfriend Lum is very jealous and capable of megavolt outputs, this tends to be a painful state of affairs. Yet they do actually care for one another as is always proven in a pinch, when the cards are finally down.
This movie best captures (I think) the general wackieness of UY, the crazy cast of characters and the frequently bizarre and surreal situations they encounter. Great closing theme as well.
3) 1988 : My Neighbor Totoro - Possibly the greatest Children's movie ever. Unless you are a complete curmudgeon, this movie will charm you and touch your heart. I'm not a Miyazaki fan, but even I was disarmed by this one. Even though there is absolutely nothing in it that could possibly offend anyone, but the most determined and humorless self appointed guardian of public morality, it will enthrall children, yet still neither bore nor insult the intelligence of a watching adult. Great soundtrack as well.
4) 1995 (the Newby of the group) Macross Plus - While the original series was terrific and possibly should be here instead. This OVA series does capture everthing that was great about the original series and updates it with some jawdroppingly well animated arial combat sequences, a terrific soundtrack and an original, creative and absorbing story.
5) 1988 : Kimagure (Capricious) Orange Road Series + First Movie - Again one of the best soundtracks of any series, extremely well done opening and closing credit sequences. Some really creative and original stories (My favorites are the TOP GUN/Godzilla movie parody episode and the Groundhog day-ish Christmas episode), psychic powers, a love triangle with lots of tension and characters you can genuinely care about set this well above the teeming masses of teen highschool romance series.
The movie has to be included since it is the true finish to the series and should not be watched without viewing the series first, since it will not mean anything to you if you haven't watched the characters struggle and suffer over the course of the series. Even though I couldn't understand a word of the movie, I was riveted to my seat like I have almost never been. The movie actually drops a lot of the humor and psychic powers of the series and focuses simply on resolving the love Triangle between Kyosuke (the boy), Hikaru-chan (the bubbly, happy popular girl who loves Kyosuke) and her best friend Madoka Ayukawa (the brooding "bad" girl who also loves Kyosuke, but won't do anything about it since she won't hurt her best friend). It really hurts watching the plot unfold, since you know and like all of the characters, but someone has to get hurt to resolve the situation and the end where Kyosuke (who is a REALLY nice guy) has to brutally reject Hikaru-chan, because otherwise things will never be resolved is painful to watch.
Runners up
Mobile Suit Gundam the Original Saga - MSG to Char's Counter Attack : It's the classic Giant robot series. I really love pieces and the ideas/world of it more than any of the individual series. Though 0083 : Stardust Memories is my fav.
Monster City - While it is, alas horribly misogynistic. It's mindblowingly cool characters and animation style set the stage for pretty much every horror manga/anime to come.
Iczer One - Again a real trend setter, with some cool characters, mecha designs and one of the stupidest villians of all time (Iczer two - When your robots are powered by emotions, the last thing you want to do before finishing off the heroes is to cruelly and pointlessly stomp on the last person left living that one of the heroes cares about).
Area 88 - Tragic hero, betrayed by his best friend and forced to fight in a war to save his own life, so that he can survive to return to the woman he loves. The most terrible part of all for him, is that he is very, very good at the Killing.
Golgo 13 (Aka - The professional) - One of the all time classic assasins, in a highly stylized movie. While not exactly a likable character you have to admire/respect his absolute ruthlessness, determination and unerring skill in carrying out his contracts. Also notable for an early use of computer animation. Note : there is a fairly nasty rape scene about halfway through the movie.
One observation, a number of these probably wouldn't have the same effect if you watched them having seen a lot of the newer stuff. These were the originals that the later stuff was based on. So much of their impact would probably be lost on more recent viewers. What has be come trite and repiditive was original and shocking once upon a time.