Basically you just asked a bunch of people to bullet point the Bible for you. In other words, the possibilities are endless.
Ruling out film, because these days it seems there aren't enough people who appreciate film to even care about it, there are many "types" of photography you could learn. I think you're going to be fairly disappointed when you get your answers but here are a few "types" of photography.
You can master the art of nature photography. This is indeed an art. This doesn't mean hang outside in your backyard until that lady bug lands on your finger. There are some real beauties in nature and to capture them takes the proper equipment and patience.
You could try out something like astrophotography. That's hooking your camera up to a telescope and taking pictures of stars. I've always been interested in doing this myself.
You could try product shots, commercial photography.
Macro is another type of photography. You can also try infrared, night photography, and panoramic photography.
The above examples are types of photography, they're not types of things you can do to a photo. HDR and Tilt-shift (in the current sense) are types of things you can do with a photo. This is why I think in a weird way you may be sorely disappointed with some of the answers you're going to get.
If you're willing to put down your digi cam for a moment you can try out other types of photography such as pinhole photography. That is always fun. Playing with a Holga is awesome fun, again ... film.