Some photo formats do lose quality. Jpeg, which is what most people save as, is. Then there are other formats, such as Tiff that are lossless. They're usually very large files. How you plan to use the photos usually determines how you save it.
I normally save things in more than one format, one jpeg that I can play with and email and such, another for permanent storage that I know won't look crummy after playing with it.
Here's one article that explains formats; there are loads of articles out there, just search on "digital photo formats" or something like that if you want more details.
Photo formats