If I had to pick a few favorites:
Armored Trooper Votoms - Easily my favorite mecha anime, even with its aged animation. I quite like how mecha here are treated as disposable weapons of war, and the generally gritty feel of the entire story and setting. That story is, by the by, quite good, but since it's a mystery, it's kind of hard to discuss in-depth without spoilers.
Serial Experiments Lain - Strange, trippy cyberpunk-esque anime that's closer to a strange arthouse film than anything else, and one which was extremely prescient (came out in 1998, for reference) in its predictions about both the growing role of the internet in society and the blending of real-life and online identities to the point of struggling to distinguish one from the other (to overwhelmingly negative results). The sound design and visuals in particular are absolutely masterful.
The Vision of Escaflowne - An "other world" fantasy story from well before the term "isekai" was common parlance among anime watchers, and for my money still one of the best. Two very likeable leads, an extremely interesting setting and story and very pleasant on both eyes and ears, it's no wonder it's endured as a classic.
Cowboy Bebop - What can be said about this one that hasn't been said a million times? Space western with interesting leads, good storytelling, well-realized setting, phenomenal sound design and a dub that set a high standard for how anime dubs ought to be done. Yeah, it's good. Real, real good.
...huh, I just realized that all of my favorites are anime-originals from the 80s and 90s. Dunno why. (Nostalgia isn't involved, since I only watched these, at earliest, around five or six years ago).
