I watch a fair bit in between work and the massive amount of other entertainment I partake in. (Manga, streams/playthroughs, and video games being the main contributors)
Personal List would have to be something like, and sorry for the long-fingeredness:
1. Evangelion
Hands down my favorite due to it being one of my first exposures, but, it also ties into psychology and Judeo-Christian religion both of which I studied as an interest.
If you haven't watched this one, I highly reconmend it.
2. Trigun
The second series I was shown and I was infatuated. There's so much to this series that I love and it actually makes me sad that it wasn't as dark as the manga. Regardless, great Hero, that imo can't be great without his astounding support cast.
Not to forget, some of the coolest and most memorable villians to appear, Knives Millions and the Gung-Ho Guns.
3. Steins;Gate
Holy ****, if Steins;Gate 0 is just as good,this series will probably take my number 1 slot.
Very underated show about A Mad Scientist, his best friend and other lab members fight against The Organization and their plot to take over the world.
Everyone needs to make TIME, watch this one. The story, plot/character development, and animation are top notch.
It's also the only anime to make me cry so, there's that. MOVING ON!
4. Gurren Lagann
Row Row, FIGHT THA POWA has basically become another motto of mine as I've always been a fan of rebellion and damn is it catchy.
A must watch for ANY shonen lover. Over the top action, epic music, gorgeous animation, and a ridiculously paradoxically written story there's only 1 complaint I could make (I dislike fan service characters, F**k you Yoko, setting women back 50 years /s)
5. Kill la Kill
Gurren Lagann 2.0 except from a female point of view. Kappa
6. FLCL
What is Fooli-cooli? who knows. Not even the characters know. Just sit down and enjoy the geniously animated short story.
7. Naruto
There's a lot people hate about Naruto. And I can understand it. However, it's still the longest running, character driven, and diverse series I've seen besides One Piece.
8. Puella Magi Madoka Magica
For a show that seems to be based on so much... uniformality, I can't help but think about how every single piece of this show was unique.
Another much watch series. And secretly tied for 7th
9. Hellsing Ultimate
*Insert Hipster Vampire saying here*
10. Panty and Stocking
I curse alot so, the dialouge taugh me some fun new things. Really good, extremely crass/crude, nothing but fun though.
Uh... 14+ and never watch with parents or people that are easily offended. Also, VERY fast paced.
Other shows I've watched but, can't make my top 10 right now are, Sword Art Online, Dragonball Z, Gungrave, Binbougami Ga, Detroit Metal City(Secretly number 11), The Devil is a Part Timer, One Piece, Sailor Moon Crystal, and more I can't recall at the moment.