I've watched quite a few anime over the years (full list here: https://myanimelist.net/animelist/whiteflame55), but picking out a top 10 is difficult for me. Used to have a clear set, but now, it's impossible to leave it to even that many. So, while I have a top 10 series (I'm giving those in no particular, though I do have some idea of how I'd rank them), I have to pick some favorite movies for a separate list.
Tengen Toppa Gurren Lagann (2008)
Hard not to love this bombastic, over-the-top series by Gainax. You might know them best by the work of another studio that spun off from them, Trigger (BNA: Brand New Animal and Kill la Kill). The animation is colorful and sharp, as in those series, but what really sets this apart is the emotional stakes baked into it and the incredible characters. It's a story of perseverance against impossible odds that always struck a chord with me.
The series that would probably top this list, it's a Greek tragedy done up in the style of mages summoning some of the greatest heroes from history to do battle over the Holy Grail. No one in this series is free from guilt, and it's incredible to watch the characters bounce off one another and challenge each other physically, emotionally and psychologically. Never had a series before that just worked on every level so well. To top it off, the studio (Ufotable) is known for their superb animations, having recently done the adaptation of Demon Slayer.
Re:Zero - Starting Life in Another World (2016, 2020-2021)
Wouldn't have said this back in 2016, but this series is incredible. It does an amazing job developing its main character, and for a show with one major gimmick (return from death), it gets an amazing out of mileage out of it. The expanding cast only gets more intriguing and the show constantly keeps us guessing as it develops, never letting us or the characters get complacent.
Made in Abyss (2017, 2020)
Another series that gets a lot of mileage out of a single gimmick, the whole series is built on the knowledge that there is a giant abyss and people go in to explore it for riches and fame. The whole series is built on the absolutely dismal realization that our lead character is after something she cannot obtain without condemning herself to death, it's really more about the journey than the destination, with every new level of the abyss being a tour de force in animation and the music being among the best in any series.
Code Geass (2006-2007, 2017-2019)
This series has a similar vibe to Death Note, though with a grander scale and mech battles to boot. The series gets going fast and focuses on a character who is caught up in a world where the British Empire never stopped expanding, and plays a deadly game of chess with people as pawns to exact revenge. Though it has its low points, it's riveting to watch the series play out, and has an incredible ending.
Cowboy Bebop (1998, 2001)
The absolute classic on this list, Cowboy Bebop is a must-watch for any anime fan. Space bounty hunters who absolutely do not get along going on adventures with an intelligent corgi and an eccentric young computer hacker, all with a dramatic and suspenseful through-line story, some great comedic side-stories, and characters whose interactions are actually more interesting than their personal backgrounds. With one of the best endings in anime and one of the greatest OPs of all time, it's worth your time.
Steins;Gate (2011, 2013)
Time travel is rarely done well, but this series bucks the trend. With a main character who is always a joy to watch and a twist in the plot that starts about halfway in, the series goes from fun exploration of a new technology to a suspenseful, high stakes thriller, this series constantly had me on the edge of my seat.
Fullmetal Alchemist: Brotherhood (2009-2010, 2011)
Honestly, I can't say anything about this series that isn't commonly known. It's the best all-around series for a reason. Everyone loves it. Watch it.
Keep Your Hands Off Eizouken! (2020)
This is the only series on this list that fits comedy and slice of life, but it absolutely deserves to be here. With some of the most innovative animation of any series, a trio of main characters who play off each other beautifully, and a plot line that never gets stale, this is a series that breaks down the process of making an anime while putting on a master class.
Mob Psycho 100 (2016, 2019)
Almost everyone should have heard of One Punch Man by now, and while that series is great, this one has it beat. Having a nearly all-powerful main character is a big risk, but this series manages to use it in an interesting and relatable way. The animation is incredibly fluid, the characters incredible, and the plot of the series, both in individual arcs and as a whole, riveting. Also, both of the OPs slap.
Onto the movies.
A Silent Voice (2016)
This movie came out at the same time as Your Name and largely got eclipsed by the other movie, despite being (in my opinion), the better of the two. Part of what makes this incredible is just how relatable its leads are, and though it's incredibly hard to watch in places, I don't think I've ever seen such an incredible display of human emotion. The animation is gorgeous, and though this is not an action set-piece, its sakuga is on par with the best shonen has to offer.
Summer Wars (2010)
I didn't expect to love this movie, but it drew me in and kept me riveted. In a story about a young man meeting the family of a friend of his and being introduced as her fiancé, the stakes quickly escalate as this story crosses over with a massive online world where a virtual intelligence basically tries to take over, wreaking worldwide havoc. The family is incredible, the animation brilliant, and the story had me on the edge of my seat throughout.
Howl's Moving Castle (2005)
Another classic and easily my favorite Ghibli film, this film manages its fantastical elements (one of the characters is living fire and another is a sentient scarecrow) while never losing track of the humanity in its leads. It has beautiful animation, and while the story can be confusing in places, it always yields meaningful sentiments that make sense of even the most outlandish of moments.