Kamichu! is an incredibly sweet-- but not saccharine --anime about a high school girl named Yurie Hitotsubashi who wakes up one morning to discover that she's now a god, in the traditional Japanese sense. The rest of her life continues on as always: her school, her unrequited crush, her friends, etc. She just also happens to be a god. And it's not some zany comedy about keeping said godhood a secret, either. It's a really stellar series. And I can prove it!
...Okay, maybe I can't PROVE it, but only because I can't find a good clip of Yurie activating her powers (by yelling "KAAAA! MIIIII! CHUUUUUUUUU!").
It was a Geneon license originally, and FUNimation rereleased it in 2008. I just confirmed that FUNi has no current plans to release the Blu-Ray...but man, I hope they do. Or maybe they could even just send their subtitles off to Brain's Base in Japan so that I could import it. Mmmm.