In your opinion list an anime (or multiple) that you believe are a NEED to watch for any new, or seasoned anime fan. My personal choice would be Cowboy Bebop.
Here are a couple that come to mind: Romance/Comedy: Toradora, Lovely Complex, Special A, Angel Beats
Romance/Harem: Shuffle!, Hyakka Ryouran
Action: Black Lagoon, Darker than Black, Full Metal Panic!
Action/Fantasy: Soul Eater, Kaze no Stigma
Psychological: Steins;Gate
I'm pretty sure the longer I stay at this post the more will come to mind so I'll stop there. :)