Okay, top 10 shows here we go. This is gonna be more of my top 10 favorites than best - there are a few shows that are cinematically amazing but I more like than love. Gonna put a little text on each I guess.. For some context, I have watched a lot of anime over the last 15 years or so and there are way more clunkers in there than good ones. College me had a very high tolerance for really bad anime.
EDIT: After finishing this monstrosity of a post, I realized I could probably do a top 50....I dont know if thats really sad or just there
1. Fullmetal Alchemist: Brotherhood
Just an all around great show. Great, realistic characters and development. Good balance of drama and humor. Some good philosophy hidden in there. Actually has a satisfying conclusion. First opening might be my favorite of all anime OPs as well. The manga is great too if you guys want to read through it. The first series isn't bad but Brotherhood really captures the underlying tension much better - and came after the manga so it follows the canon story.
2. Ghost in the Shell: Stand Alone Complex
The show can be a real mindbender at times. One of the best sci-fi across all media in my opinion. You can really see the influence this had on the original Matrix film. The 95 movie is just as good and 100% worth a watch if you have a few hours to kill. Season 2 (2nd gig) is pretty decent too, but not as good as the first.
3. Samurai Champloo
4. Cowboy Bebop
Grouping these together since they are mostly by the same creative team. Both are character driven odd balls as a Space Western and a Hip-hop themed show about samurai (with one of the best baseball episodes in anime). Champloo has a bit more coherent of a story and had more humor of the kind I liked, but honestly both are masterpieces. Both are usually two of my first three recommendations for friends looking to get into anime (along with FMA:B).
5. Tengen Toppa Gurren Lagann
Easily one of the most ridiculous anime ever made. Super funny and makes you feel really good about life. Its the polar opposite of Evangelion in a lot of ways but both are about mechs at least. Never fails to make me laugh
6. Shinsekai Yori
I think the most obscure show on this list so far. This show is a huge mind screw from start to finish. Just a lot going on here but asks some very interesting philosophical questions. This is definitely not a show for everyone. It can be a bit slow at the beginning especially, but the pace gets going very quickly. Highly recommend.
7. Clannad
Mainly here for the second season. A surprisingly sad romance which is not that uncommon (also take a look at Your Lie in April which would make my top 20). Its good. Key does a really good job with all their shows. I would also recommend Angel Beats (another top 20 candidate) and Charlotte.
8. Steins; Gate/Puella Magi Madoka Magica
Really interesting premise and overall great shows. Yes, its a double spot - I have a hard time separating the two for reasons that I can't explain without plot spoilers. I mentioned earlier that I think Steins;Gate drags a lot in the middle. Madoka drags a bit at the beginning. The end is absolutely worth getting to. You can skip Steins;Gate Zero.
9. 86 Eighty-Six
Seasons one and two have totally different flavors and are both really really good. Season one is survival horror and season two is more a war story. A character driven show with a terrifying premise. I think this is the most recent show on here by about 5 years or so.
10. Yu Yu Hakusho
Was a favorite growing up and aged surprisingly well. The quintessential shonen in my opinion (along with the original Dragon Ball). Has the best tournament arc in anime (Dark Tournament) and in classic Togashi fashion the story kind of meanders around as we get along with it. Personally, always liked this more than Dragon Ball and would recommend anyone who wants a classic battle shonen with some demons involved to take a look.
Picking the first 4 for this list was pretty easy for me. I knew 5-8 but took a while to finalize the order. 9 and 10 were a lot harder. Ill tack on a several honorable mentions to complete this I guess.
Hardest exclude for me was Mirai Nikki. Definitely my guilty pleasure anime that I rank much higher than it actually should be.
Hunter x Hunter was hard to fit on the list but I really wanted to. I think the manga is better than the anime (2011) but both are pretty solid. Togashi's writing really carries this series and his planning arguably hampers it a lot.
Angel Beats and Your Lie in April were mentioned above. I think Toradora! would be my other pick for the 4 best romance anime in some order.
For your inner edge lord, Tokyo Ghoul is gruesome and quite solid. Horror anime is a bit lacking in general but Another was pretty good.
Sports anime has some solid shows (Ace of Diamond, Aoaishi, Slam Dunk) but I don't know that any would break my top 20. Ace probably comes closest.
Mob Psycho was worth the hype that its sibling One Punch Man got. Both are hilarious though.
Some other more obscure stuff thats worth checking out: Barakamon, Sagarda Reset, March Comes in like a Lion, Land of the Lustrous, Chihyafuru.
And even though this top 10 has ballooned out a lot, I don't think I can leave out one other anime: One Piece. Yes, I know its long. I have literally been reading it since 2007 and somehow it still has maintained its quality (looking at you Naruto and Bleach).