My personal favorites in no particular order:
Bleach(yeah yeah it sucks now but when I started it was godlike)
Naruto(has been good most of the time)
FMA(both series are amazing)
Gungrave(first anime I ever finished so a personal favorite. Is recommended to anyone starting out on anime)
Historys Strongest Disciple Kenichi(really nice old fashioned series, haven't seen a mention of it here. Full of action and comedy and its 50 episodes!)
Death Note(probably should have ended when a certain character died but still one of the greats)
Code Geass(an obvious entry)
Darker Than Black(great animation, really smooth action)
Claymore(a very different series, dark and serious full of action and blood)
Clannad(funny and sad at the same time, maybe not for everyone but its really good imo)
School Rumble(its hilarious man, anyone who hasn't watched this series has got to give it a go right now)
Lucky Star(only for people who have watched quite a lot of anime before hand as it has many parodies of other anime and references to japanese culture)
Bakemonogatari(only for Senjougahara~_~)