I would say Wolf's Rain, but that might be a little too dark for what you are looking for right now. If you're interested, though, it is a show of four wolves trying to make it to paradise and all the other characters that are connected to their adventure in some way. Overall, it has a good story (though the OVA sort of hurt the ending), memorable characters, and an incredible soundtrack. It's still one of my favorites, and if you don't mind a semi-dark series (it's on the darker side, but there's worse out there), I cannot recommend it enough.
After that, there is:
Baccano!: Despite the serious premise, the show still manages to not take itself too seriously. It's got an interesting plot and lively (albeit static) characters. While it is darker at times, it does manage to stylize itself so that it goes hilariously over-the-top, and quite a few characters serve well for comic relief. Really, it is just a fantastic balance of both.
Beyond the Boundary: If you liked Bleach, then I'd imagine you would like this, as they have a lot of similar concepts in their worlds. Just be warned that, unless there is a second season (which is unlikely), there are a few unanswered questions. Most of what you want to know (based on what the show focuses on) is answered or implied, though, so don't worry too much.
Sword Art Online: Like pretty much everyone else, I would recommend at least watching Season 1.
Log Horizon: An ongoing show similar to SAO in concept, but the two have taken drastically different directions. Log Horizon goes rather in-depth with the concept of understanding an unfamiliar world and how societies are built, especially when compared to SAO. It doesn't focus much on action preferring to focus on character interactions and politics. Still, it does manage to have a little action (granted, the action isn't very good), and it also has quite a bit of decent comedy as well. Just be warned that the first few episodes are absolutely terrible. After that, though, it manages to work out its problems, focus on its strengths, and offer an interesting show.
Golden Time: Another ongoing show. If you don't mind romantic comedy, this is actually a very good one. I would at least watch Season 1. Season 2 just started and, if the first episode was anything to go by, it might be going downhill.
