The following are some image formats that can be saved from within Photoshop, using the "File --> Save As" command. JPG, GIF, and PNG formats can be previewed before saving if you use the "File --> Save for Web and Devices" command.
The "big three": Most of the time, you'll use PSD, PNG, or JPG files. Many Photoshoppers will use JPG for sending pictures to friends, PNG to save a "perfect" archival copy of their image (though sometimes RAW is used for this if it's a photo), and PSD for working in Photoshop.