I recognize too many films for my own good, so here I'll just give the top 10 recommendations from off the top of my mind.
1. Eternal Sunshine of the Spotless Mind (Fantasy/Romance/Drama/Sci-Fi) - Stands as one of my absolute favorite movies. Watch it and absorb it. It's mind blowing. Absolutely incredible, it's acting, direction, scriptwriting, cinematography, everything stands and rises. It's almost infinitely watchable.
2. WALL-E (Sci-Fi/Animation/Drama) - It's breathtaking. Watch it and love it. Of course, you probably already have. I'm placing it in the slim chance that you haven't watched it yet.
3. District 9 (Sci-Fi/Drama) - It's fascinating, if not a tad bit racist. It's worth a watch if you even remotely like this sort of stuff.
4. A.I. Artificial Intelligence (Sci-Fi/Drama) - Incredible sci-fi movie. It's heartwarming and creatively done, integrated with so much passion in it.
5. Crouching Tiger Hidden Dragon (Martial Arts/Action) - You like Martial Arts? This is a must-watch. A spellbinding triumph of story, action and style.
6. Mulloholland Drive (Mystery/Thriller) - A spellbinding modern noir thriller that is a must-watch if you like the genre. It's compelling and balanced, while also being extremely well made.
7. Spirited Away (Fantasy/Animation/Drama) - It's Spirited Away. If you haven't watched it, go. Do it now.
8. Memento (Mystery/Thriller) - Film noir at it's finest, I implore you to watch it right now. It's finely structured and well made, filled with surprise and amazement.
9. Pan's Labyrinth (Fantasy/Drama) - Incredible, artsy, spooky, and an artistic spectacle at it's peak. It puts you in it's own setting and never lets go of you.
10. The Incredibles (Adventure/Animation) - A film that sits comfy near the peak of the Pixar canon. Never has a Pixar film so effectively captured the concept of human emotion quite as well as this one has.
... GRAH! I just have to give more. Forgive me.
11. Waking Life (Fantasy/Animation) - You like Inception? Then prepare to be spellbinded by this animated rotoscope film that places viewers into a total trance.
12. Zodiac (Crime/Thriller) - A compelling crime thriller that is an absolute must watch if you like it when movies demand your interest.
13. The Social Network (Drama) - This falls into the "mindblowing story" area. It's not fantasy, not sci-fi, but it damn captures the feel of one very well. It's stylish, aesthetically pleasing, and highly compelling.
14. The Departed (Thriller/Drama) - Again, in the "mindblowing story" area. It's incredible screenplay well complements the talents of it's regarded director. It's impossible to not find this incredible.
15. Winter's Bone (Mystery/Drama) - Gets under your skin. It captures emotions so beautifully, yet it's so unknown. What a shame. It's lead is unquestionably effective in her performance.
16. Star Trek (Sci-Fi/Drama) - It's (dare I say it?) the best retelling of the Star Trek series to the big screen.
17. Lost in Translation (Drama/Comedy) - Another "mindblowing plot" movie. It's a poignant romantic comedy set against the backdrop of a beautiful modern Japan.
18. How To Train Your Dragon (Adventure/Fantasy/Animation) - It's probably Dreamworks Animations' best film yet. It's definitely worth a watch.
19. 2001: A Space Odyssey, The Thing, Star Wars Original Trilogy (and III isn't too bad either), Terminator 1 and 2 (Sci-Fi) - Some older sci-fi movies that I placed in one spot. If you'd find that you'd like to watch one, here they are.
20. Oldboy (and the rest of the vengeance trilogy), Confessions, Kill Bill Vol 1 and 2, Requiem for a Dream, A History of Violence, Inglorious Basterds (Action/Drama) - These are all the more gory movie I wanted to suggest, but couldn't. In the event that you find that you'd want to watch one, go ahead. Just leaving these out there.