Old wallpaper that is in good shape does not need to be removed before new wallpaper is applied, according to About.com. However, if the old wallpaper is greasy or damaged, it should be removed.
For old wallpaper that looks good, About.com recommends cleaning with trisodium phosphate before it is wallpapered over. Damaged or greasy wallpaper can be removed by getting the edges wet and letting the wallpaper absorb the water. A plastic scraper should be used to scrape the edges from the bottom up, and drips should be cleaned immediately. Clothes steamers, white vinegar and commercial remover are also options for removing wallpaper.