Personally I'd recommend a lot of the Kyoto Animation shows. They seem to consistently release great anime.
The Melancholy of Haruhi Suzumiya and the Movie The Disappearance of Haruhi Suzumiya , both seasons are great even though the second season had that blunder with the "Endless Eight" debacle it was great nonetheless, and that movie, Oh.My.God. That movie. It was perfection, or something very close to it. I'd recommend anybody planning to watch the series, to do so in the English Dub as the dub was amazingly well done, and an especially great performance by Crispin Freeman who was the voice of the protagonist, Kyon.
Hyouka as well. Great mystery anime with some very interesting characters and also a hint of romance thrown in there. The animation quality is also really good. Sadly there's only the one season, so far anyways.
K-ON! was also very entertaining in my opinion. I know that it's definitely not for everybody with all the moe stuff and what not but I found it really enjoyable, the English dub is very good too.
I also just recently finished Chuunibyou demo Koi ga Sh*tai! and I absolutely loved it (Excuse the unfortunate censor). Very interesting and funny story, loveable characters, and some very cute romance between the two main characters that could make anybodies heart melt.
There's more anime I'd name that's not just from KyoAni but I think this post is long enough already, maybe I'll post some other ones later.