If you have wallpapered walls that you would prefer to be painted, you may be able to do so without having to remove the wallpaper first. While it is not recommended that just any wallpaper be painted over, as it can look messy and unprofessional when finished, a wall that had bare drywall or unprimed flat paint before that wallpaper was applied would be so difficult to remove that the better option is to paint over it. With the right supplies it is possible to achieve a well-done finished product.
Paint - Just about any paint can be used on a wallpapered wall that has been properly prepared and primed. However, there are certain paint types that may be more efficient than others at hiding the flaws typically associated with a painted-over wallpapered wall, such as those found on areas that have been taped over. The best way to hide these flaws is by using a flat paint or a satin sheen paint on your walls as opposed to a semi-gloss paint, which may actually highlight the flawed areas due to its shine.
Primer - Perhaps even more important than the paint that you use on your wallpapered wall is the primer that you put on it first. Unlike the paint, which can be just about any flat or satin sheen paint, the primer needed is more specific. To cover a wallpapered wall, you will need either an oil-based primer or a shellac-based primer, both of which are particularly good at covering stains, so it will cover the patterns of your wallpaper more efficiently.
Other Tools - In addition to the proper primer and paint, there are other tools that will help you get the job done right when attempting to paint over wallpaper. Besides the usual necessities like paint brushes and rollers, drop cloths, and painter's tape, you should also buy a small container of spackle, some fine-grit sandpaper, and a small container of wallpaper adhesive. You should also purchase a large sponge, like the ones used to wash cars, and a small bucket.
Preparing the Wall - There are certain measures that should be taken in order to ensure your primer and paint will stick to the wallpapered wall. First, fill your bucket with warm water. Then dampen your sponge and wipe down the entire surface of the walls. This will remove any residual wallpaper glue as well as moisturize the possibly brittle wallpaper. Once the walls have dried, test a small area of the wall with the primer. If it dries smoothly, you are good to go. Lastly, before beginning the priming and painting process, repair any uneven areas on the wall with spackle and sandpaper and fix any peeling wallpaper using the wallpaper adhesive.