My short list of ones I actually remember:
Ouran High School Host Club
This isn't good cause it's good. It's just a good time to laugh at. It has some good moments of seriousness, but most of the time it's busy making fun of itself which is a good time
Angel Beats
I cri at the end. It's good.
Attack On Titan
It's a lot fun. Especially the new OVA's (Birth of Levi and the other one that I forget)
Clannad
Probably one of the most know/recommended anime. It's good. It has some flaws, too much crying from the cast, some stupid arc points, but it and after story are a pretty good set.
The Irregular at Magic High School
This is a fun one too. It does a good job of doing both funny and serious. I haven't finished it yet but it's good so far.
Kotoura-san
This is definitely a cutesy anime. It's still really good and gets decently serious at times, however most it revolves around a perverts thoughts and a mind reader freaking out about them.
The Devil Is a Part-Timer!
Watch this. It's fucking hilarious. The beginning makes zero sense as there's no subtitles for whatever language they're speaking. You can usually guess though.
Date-A-Live
Another fun one. Not really sure what to say, it's people beating each other up. Little fan servicey at some times, but most anime do too.
Bleach
I know I know like 80% of this is filler and crap.
But the first 2-3 season (Whatever it is before the Bounts), The Zanpakto arc, and when they finally get back to the Espada fights are actually pretty good. The filler sucks, but it has a few good arcs.
Madoka Magica
Didn't finish this one either but from what I have watched it's good. It's about Magical Girls..... so yeah. Take from that what you will.