1 - Don't just photograph the tree. Even if it's a really cool-looking tree, just taking regular lighting, slapping it in the frame, and hitting your shutter release is a recipe for a boring picture 99% of the time. Find what interests you about the tree (the shape, the color, etc.), and find a way to focus on that!
2 - Play with the lighting. When used carefully, side lighting can make for some really nice shots. It's especially effective if you're trying to emphasize the texture of the bark (or any texture, really). A nice silhouette with a dramatic sunset in the background can work wonders if the tree is particularly nicely shaped. Experiment.
3 - Get in closer. Something about how I'm hardwired makes me automatically want to try and find a way to fit the entire tree in the frame. Often, however, your picture will turn out better if you zero in on a specific aspect of the tree.
click to enlarge, or see it on Flickr
This photo was taken in open-shade lighting, which gave me a nice balanced look between texture and harsh shadows. The texture looks good because I'm pretty close to the tree, but the real focus of this shot is the odd lichen/moss growths on the trunk. From further back, it's hardly noticeable, and this tree looks boring. But once you get in closer, details like this tend to jump out.
Have some examples of good tree photos? Post a link in the comments!