JPEG, GIF and PNG can be displayed with the img tag and will work in all browsers, the object element can be use for displaying images specifying its MIME type, but what oth
There's an excellent chart on wikipedia that lists common image types and their support by browser.
The file types you listed (jpg, gif and png) seem to be the main formats supported by nearly every browser, albeit with certain caveats:
Internet Explorer supports PNG images but is unable to correctly display images with gamma correction or color correction. Versions of Internet Explorer prior to version 7 are unable to correctly display images with alpha channel (for transparency) without additional coding
BMP will work most anywhere.
But for web work, you should probably stick to the three you listed in your question.
Until 2006, IE didn't deal properly with PNGs that used the alpha channel, while Firefox and other (nearly) standards conforming browsers did. There is still a lot of IE 6 out there, judging by my apache logs.