Ugh, that's gonna be hard. The main problem is that I only recently started watching anime again and I pretty much forgot most of what I watched before that. Though I'm willing to give it a shot.
This list only includes TV series (if it were movies, they would probably take all 5 spots).
1. Neon Genesis Evangelion - Good or bad this one is the original Emotional Roller Coaster for me. I have watched it so long ago, but it still sticks with me even now.
2. Death Note - Really liked the concept and execution, though season 1 was by far superior to season 2.
3. Code Geass - Again, liked the concept and execution. Solid series throughout.
4. Kyoukai No Kanata - Beyond The Boundary - Liked it
5. Guilty Crown - Not too sure about this one being here, but it left an impression on me
Kyousougiga was in contention for 5th place.
Samurai Champloo as an honorable mention.
I probably forgot about some anime I watched years ago as I used to watch a lot, before I completely switched to manga, but if I forgot them they probably don't belong on the list.
There you go, not the most revolutionary list and you probably watched them, but this is what I like.