Gone with order of release, and it was tough to choose.
1. Battle Royale - 2000
Along with Princess Mononoke (which I'm not listing as it was 1997, even though I loved the dub), the film that got me into foreign films. It was just unlike anything I'd seen before - it's stylish and dark, but with utterly surreal touches.
2. The Lord of the Rings - The Fellowship of the Ring - 2001
This was just such an achievement. I knew so many people who loved the books, but the idea that there could be a version made that would make all of us nod and go 'yep, that's Gandalf, that's Aragorn, that's the Shire...' seemed ludicrous. But it all came together, and did so in a way that redefined event cinema.
3. Secretary - 2002
While you could go in assuming that it's going to be a dark kinky sex film, it's actually a surprisingly sweet, old-fashioned romantic comedy. Along with Shortbus in 2006 (which is another 'bubbling under' one), it also used sex to talk about mental health, depression and loneliness. The two leads are fantastic, and it's funny and sexy.
4. Casino Royale - 2006
Daniel Craig is a fucking fantastic Bond and it's a shame that most of the films haven't lived up to his portrayal. But Casino Royale - holy shit, it was just the coolest film of the decade. Stripped everything back perfectly.
5. The Prestige - 2006
A silly film, but one with enough style and confidence to carry it off.
6. Zodiac - 2007
I love true crime, Fincher and slow-building-tension, so what wasn't to love about this? Absolutely absorbing and great cast from top-to-bottom.
7. Hot Fuzz - 2007
As @Hannibal Scorch said, it's so close between this and Shaun of the Dead. But Hot Fuzz went and did something harder than Shaun - the tropes weren't as obvious, and it still managed to be utterly satisfying. And it's funnier.
8. The Wrestler - 2008
I don't know anyone that hasn't loved this film. I don't know if it'd still be on the list if it wasn't this place - but it'd be bubbling under. In terms of 'films that feel like they were made for me personally', this is right up there. It's just beautiful. Any film that can have so much going on in it that Marisa Tomei naked isn't the first thing I think about is doing something astonishing.
9. Anvil: The Story of Anvil - 2008
Halfway through watching this, my girlfriend and I were briefly convinced it was fake. It's just SO Spinal Tap. But it's also funny as hell and touching. I showed it to my parents, and my mum was aggressively disinterested in the idea, but got into it - by the end, she was watching with her hand over her mouth, ready to burst into tears if the final gig didn't get a good turn-out.
10. Four Lions - 2010
This is here as much for Chris Morris's previous work, but Riz Ahmed is brilliant in it as well. Genuinely funny, but doing that Morris thing of taking something complex and important and exploring it under the guise of silliness. Rubber Dinghy Rapids, Brother.
11. The Artist - 2011
It's a love-letter to cinema. Just beautiful, funny, sexy, smart... I remember my girlfriend and I went in after a bad day, a bad journey and a long wait at the ticket-booth, five minutes late, and annoyed when we sat down. And within five minutes, we were swept away.
12. Whiplash - 2014
Fuck, fuck, fuck. I've seen horror films that were less tense than this thing. JK Simmons is just incredible in it, and the final scene is just pure film - music and visuals and storytelling.
13. The Babadook - 2014
My film of the decade and Essie Davis being overlooked for even an oscar nomination is just further proof of how much horror is despised by mainstream critics. An astonishing performance in the middle of utterly beautiful horror.
14. Spotlight - 2015
Partly, this just hit home so much about how much power the church held over Catholic communities. I'd been doing a month sober when I went to see this, and it was the last day, and I needed a drink afterwards.
15. Get Out - 2017
I liked Us a lot, but Get Out just hit so many things perfectly for me. It's funny, it's nasty, it's genuinely unsettling... seeing it become such a success was lovely. I saw a preview of it with an audience that happened to be almost exactly half white and non-white. It was fascinating watching how each part of the audience reacted differently to some parts.
16. I, Tonya - 2017
Margot Robbie is just incredible in this. It also does a great job of taking a big, complicated story and telling it well. One of the best-written films in terms of that.
17. IT - 2017
A shame the follow-up sucked, but I'm a huge Stephen King fan and this was a better adaptation than I expected.
18. One Cut of the Dead - 2017
Probably the least-seen film on the list, but it's just so much fun. Utterly bonkers and keeps building and building in terms of comedy. Also, utterly unlike anything else.
19. BlaKkKlansman - 2018
Totally echo what @RedRooster said.
20. Avengers: Infinity War - 2018
Man, this was a tough one. The criteria I sort-of went with was 'did any other film do what it did better?' - which was why Four Lions beats out Death of Stalin, and Hot Fuzz and One Cut took out Shaun of the Dead. But I was wavering between this, Winter Soldier, Dark Knight and Iron Man. But I've never been in a cinema that reacted the way it did on the opening night at the end of Infinity War. There was genuine shock and reactions, and it's one of the best audience reactions I've EVER seen. So for that, it finishes off the list.
Man, 2017 ended up being a hell of a year. Also, I've somehow ended up not including any Miyazaki or Pixar. A bunch of very good stuff bubbling under too.
Film of the 2000s: Zodiac.
Film of the 2010s: The Babadook