The number one reason that wallpaper peels is due to high humidity. So if you have wallpaper that is starting to peel, try to address the humidity issue first. For example, do you need a better exhaust fan in your bathroom or kitchen to keep the humidity down.

If you've done all you can for the humidity, the next trick to try is sealing the edges of the wallpaper. Doing this will keep humidity from being absorb by the edges of the wallpaper (that's where the water gets absorbed since it's an unfinished exposed edge). To seal the edges of the wallpaper, get clear varnish and apply a single thin coat of varnish to the joints where the wallpaper meet. There are many types of finish to varnish (gloss, matte, etc) so make sure you get the same finish that you have on the wallpaper so that the varnish will not be noticeable.