A list of several different image types is:

-Bitmap
-GIF
-JPEG
-PNG
-TIFF

Each of these will be explained in detail. The best one to use however is PNG (see LIJI's article: http://create-games.com/article.asp?id=1865 )

Bitmap (*.bmp)
Bitmaps are uncompressed images. They do not retain alpha values. Any transparent areas on your image will appear white. Bitmaps are quite useless for anything now.

GIF (*.gif)
This format is lossless and retains alpha values. However it is either transparent or opaque. It doesn't retain any "in-between" alpha values. This format is good for animations and websites that don't require varieties of alpha levels.

JPEG (*.jpg *.jpeg)
This format is a lossy format and will lose quality when edited and saved. It doesn't retain alpha values either and all transparent/semi-transpaarent areas will become white.

PNG (*.png)
This is the God of all image file types. It is compressed AND is lossless. It also retains ALL alpha levels. This means that it can go from 0 (transparent) to 255 (opaque). This file type is great for its small size and great quality.

TIFF (*.tiff)
This image type is lossless and retains all alpha values from 0-255. However it is not as widely supported as PNG.

All of the above image types are accepted by photobucket and imageschack (with the exception of TIFF which is only supported by imageschack (I said it was less supported right ))