Files of any format can be stored in Asset Bank. It supports (i.e. can convert) all popular image formats, including JPEG, TIFF, PNG, GIF, EPS, PSD, AI, PDF.
In general, you should upload only one version of a particular image. This should be the highest resolution version you expect to ever need in the future. Asset Bank will resize and reformat images on the fly according to users' requirements as they download them, so you don't need to add multiple sizes of the same image.
Rasterised Images (i.e. those made up of pixels) can easily be downsized, however they can't reliably be upsized (information cannot be 'created'), hence the need for the highest resolution originals.
It is usually best to leave your images in the format they are in. Otherwise you risk losing information in the conversion- users can perform the conversions they want in Asset Bank when they need to. In particular:
Never convert from a lossy format such as JPEG to a lossless format such as TIFF. You won't gain anything other than a larger file size.
Don't convert RGB images to CMYK. Many users will just need to convert them back to RGB, and anyone who wants an image in CMYK usually knows what they are doing. (Asset Bank handles colour-profile conversions for users).
Circumstances when you might want to convert images before uploading them, are:
Your images are in a non-compressed format such as PSD, BMP, TIFF and you either a) have limited disk space on the server or b) want to reduce bandwidth when users download the originals (or both). In either case, you would probably benefit from converting these images into high-res JPEGs. If you need a lossless format then you could consider JPEG 2000.