I've talked about some of these before, but here's my top ten. Also, this post is going to be long. You've been warned.
1. Cowboy Bebop
Might be an obvious choice, but I have yet to find another anime that I love as much as this one. Bebop has fantastic animation, great characters, an amazing soundtrack and dub, and overall just never fails to bring a smile to my face. Following a bunch of bounty hunters through their adventures in space, this series is absolutely timeless and I doubt anything will ever come this close to perfection. Infact, if it weren't for one episode ending with a cliffhanger that's never resolved, I would call it perfect.
2. Fullmetal Alchemist: Brotherhood
Fantastic shonen that has many of the same strengths Bebop has (animation, voice acting and characters), yet is a completely different show. Some of the best fight scenes I've ever seen can be found here, along with a gripping story and lots of character development.
3. Gintama
I feel like I'm repeating myself here, but I'll say it again: Gintama is the most hilarious show in existence. Originally about a samurai in an age of alien invasion and how he and his two sidekicks make ends meet, the show soon went on a lengthy tangent and never looked back. Gintama has originality in spades, many episodes being downright absurd, only for a serious arc to flip the tables and deliver gripping action all of a sudden. There is no other show that does what Gintama does, and the quality has been consistently high for years. It's incredibly self aware, regularly breaks the fourth wall and won't shy away from breaking taboos (not many animes will blatantly mock politicians like Gintama does), but it always finds time to tell a touching story aswell.
4. Paranoia Agent
Creepy tale about a juvenile delinquent that hits people with a bat when they feel like they're driven into a corner. Or so it seems. I still haven't completely wrapped my head about what really goes on in this show, and that's what makes it so fascinating. Paranoia Agent really lends itself to different interpretations and is very thought provoking, but also is just really entertaining to watch.
5. The Melancholy of Haruhi Suzumiya (Season One)
Haruhi is such a weird show, because it does so many things at once that it can be mindboggling. I love series that turn out to be completely different from what they initially seem to be, and Haruhi is a prime example of doing just that. Most people will probably know what it's about already, but I'll refrain from spoiling it for those who don't. The second season is very disappointing, having only really one good episode followed by an arc that's basically the same episode eight times (no really) and another where the main character is completely insufferable. The first season, however, is magic, and I cannot praise it enough.
6. Monster
A criminological thriller with a very dark atmosphere that tells a fascinating tale about a doctor who unwillingly created a serial killer, and is trying to undo just that. Monster is ruthless in its depictions of very realistic tragedies and rather bleak, but the storytelling is so good that it pulls you in and never let's go until the end.
7. When They Cry
This is the most gruesome, soul-jarring anime I've ever seen (Elfen Lied doesn't touch it, neither does Gantz) but it's incredibly good. Each year, during the Cotton Drifting Festival, one person dies and another disappears. Keichi, who newly moved into the rural town of Hinamisawa, is dragged right into these events that happen again, and again, and again. Every four episodes, infact. The whole first season is a complete mystery that repeats the same time period around the Cotton Drifting Festival, but, while the outcome is always very similar, the way these things happen are different every time, or shown from another perspective. The second season is what really makes this show good, because it wraps it up nicely and everything actually makes sense in the end. This one is sometimes hard to watch, but it's so worth it. Also has a kickass theme song:
8. Azumanga Daioh
The plot can be summed up as follows: It's about high school girls. That's all of the plot there is to it. What sounds really boring and generic is actually a character driven masterstroke of comedy that's very lighthearted, incredibly funny and really, really, dare I say it, cute. The show follows a group of high school girls, all with distinct personalities, through their daily lives. Ocassionally bordering on the surreal, the humor consistently hits the mark and the show never fails to pick me up.
9. Time of Eve
This very short series wonders what life would be like if robot servants really existed - do they have feelings? Can a human "love" his robot? What happens when a robot finds a safe place outside their masters' gaze where it can just be themselves without restrictions? Time of Eve delivers the answers in a fascinating manner.
10. Ranma 1/2
Finally, this one had to be on the list, even though it's far from perfect. It's what originally got me into anime, and yes, it's because there were nipples. I was a horny fourteen year old, is what I'm saying. Ranma falls into a cursed spring and from that moment on turns into a girl whenever he's splashed with cold water, and back into a male with hot water. Further complicating things is his arranged marriage to Akane, daughter of the Tendo Dojo for brawls of all kind. The premise is ridiculous, and so is the show itself. But it's also really funny, and genuinely heartwarming at times. It takes a nosedive after a while when the plot gets stale and stops moving forward, and the animation isn't the best, but I love this show and am unashamed to admit that it's on the list for nostalgia reasons.
Now I really am not trolling here, but can I ask what about this film you liked so much to make it your number three spot? I've seen praise everywhere for it and I thought it was the worst anime movie I've ever seen to be honest. That scene where the grandma phones up all of her relatives for ten minutes straight almost made me turn it off, and when the film was over, I wished that I had. Incredibly dull, boring movie.
Yuru Yuri (it's really not what is sounds/looks like, its just a small anime to enjoy)
I watched three episodes of that and had a really hard time in deciding wether to keep watching or drop it. On the one hand, it was hilarious sometimes, yet on the other, I felt like such a pervert watching it. Like, even more than I normally do.