Always remove old wallpaper, no matter how intact it is. Eventually, it will pull away and tear in places; even just microscopic tears will affect whatever you put on top. The only exception would be if the builder put paper over drywall without priming it first and you are actually removing chunks of the drywall. If you paint over wallpaper, the seems will remain and may even become pronounced. Plus, your paint may not adhere evenly to the paper depending on what wallcovering was used in the first place.
To remove wallpaper, first try spraying it with very hot water and scraping it. Many prepasted papers come off fairly easily. If that doesn't work, you can buy a scoring tool and solvent. Many people also have luck renting a steamer from the local home supply store.