This is in an incredibly rough order, but in general these are kind of my favorites.
1. Neon Genesis Evangelion (include the movie End of Evangelion in this since it's technically the end of the series): Other than DBZ and Pokemon this was one of the series I for super into when I first became obsessed with Anime. Between two video stores I rented all the VHS tapes over the course of about a year to watch it all, and loved most of it.
2. Dragonball Z: This is the show that got me into Anime and I am forever indebted it for that.
3. Cowboy Bebop: no explanation needed; it's a masterpiece
4. Ghost in the Shell: I'm referring to the original movie, not the TV series. Everytime I rewatch it I seem to love it more than he last time I saw it.
5. Mobile Suit Gundam: 8th MS Team: I haven't watched a ton of Gundam, but really liked this series' more grounded and flashy approach to the franchise. Not too long either and has a great story.
6. Princess Mononoke: My favorite Ghibli movie, gives me chills every time I watch it.
7. Claymore: Sadly this anime falls apart in the last two episodes, but every episode prior is excellent.
8. Whisper of the Heart: My second favorite Ghibli movie, this one always leaves me in a good mood after watching it. Also it's a very inspirational movie about following your dreams.
9. Pokemon: This might be in my top 10 mostly due too nostalgia, but I still adore this anime, at least up through the Johto League Championship episodes.
10. Outlaw Star: Just an excellent, classic anime.
