Are there any formats other than Gif that support transparent portions of the image?
If you’re talking about on the web, the only alternative to GIF is PNG. Unfortunately, transparency isn’t supported very well by IE, so you’re mostly SOL.
Not that it’ll do any good, but here’s a petition for MS to include proper PNG support:
http://www.petitiononline.com/msiepng/petition.html
As for other formats, there’s loads. Most decent graphics programs have their own native format with some form of alpha transparency: PSD for Photoshop, XCF for the Gimp, &c.