Yes, JPEG is lossy, just like MP3 for audio. So it's really just a distribution medium. Your camera (unless you paid a lot more for it than I did) probably only produces JPEGs - that's OK for the first generation if you save at high resolution and best quality, but you lose some every time you produce a new JPEG from that. So I usually keep the camera stuff separate from the presentation stuff, and save the ones worth keeping as TIFF (which is lossless, like a ZIP file) before messing with them. Audio is much the same - WAV and FLAC are lossless so they're good for archiving; MP3 and most of the other formats used in your iWhatever ARE lossy and are good for one shot only from the original if you want anything even remotely resembling quality.

GIF was not designed for high quality graphics. It has a limited color range and does compression. It's good for dancing whatevers on your web page though.