Jeez, it took a while to really narrow down my choices. The last time I tried to give a top 10 list to someone, it ended up being a top 15, simply because of the variety of series that I like.
Some honorable mentions that I was considering including but I didn't:
Clannad
Code Geass
Baccano
Durarara
FMA: Brotherhood (I think it's better than the '03 series by a long shot)
Sunday Without God
Little Busters
NouCome (AKA My Mental Choices are Interfering With My School Romantic Comedy)
Fate/Zero and Fate/kaleid Liner Prisma Illya
One Week Friends (it's not yet over and I want to see how it ends before including it in a top anime list)
No Game No Life (same as above)
Hyperdimension Neptunia the Animation (truthfully, I've never seen the whole thing. I kinda want to watch it with someone, but haven't gotten the chance to yet.)