well lets see it in categories (whatever mood to watch you are in)
action:
- Black lagoon
- Berserk (if thats not classic, what is?)
- Claymore
Story:
- Death note
- Code geass
- Welcome to the NHK (i recommend you watch several other shows before watching this)
- Higurashi no naku koro ni (you HAVE TO love the twin sisters arc)
Funny:
- bake&nisemonogatari (dialogues are REALLY funny, if you dont get it or cant follow, dont blame those awesome shows for it)
- katanagatari
- Lucky Star (watch several others before, you could end up thinking its a waste of time, but many many ppl really enjoy it)
If you love yandere:
- mirai nikki (usually a 6/10, but gasai makes it like 9/10)
- school days (may be not THAT good some ppl could say, but it really hit me emotional. First episodes were a quite sad lovestory, and afterwards hatred rised in me more and more until the end)
Emotional:
- Elfen Lied
- Girl who leapt through time
things i think you should evade/keep in mind:
- noein (waste of time. its just goes on far too long, no substance left after ~10episodes)
- blood+ same was noein, story was promising, but couldnt fill 50 episodes and therefore became shitty
- if you watch BRS watch the OVA first!!
- gantz (never understood what ppl find in this show)
- unlimited blade works (just dont do it)