If you have the time, removing wallpaper prior to painting is the best option. But if you aren't able to renove the wallpaper for whatever reason, you can paint over it if you follow some simple rules for painting over wallpaper.

First, you need to make sure that no corners or seams are lifting. The paint will crack because of the movement of the paper. So no, painting over wallpaper isn't a good idea if your wallpaper is in rough shape and it's easier than removing it. Securely glue any corners or edges and allow to thoroughly dry.

Next, you will want to paint over the wallpaper with two coats of stain killing primer-sealer. This will cover the pattern of the wallpaper so you won't see the design through the top coat of paint. Regular primers will not do the trick that stain-killing primers do, as they are not fomulated to cover any patterns beneath the paint.

Once you have your two coats of primer done and dried, check the seams or any other imperfections that the wallpaper caused (such as other holes etc). Use a high grit sandpaper (such as 400 or 600 grit) to file down the seam so it is not noticeable.

Now it is time for your main coat of paint. Just paint over the primer like usual. Allow to dry and now you have perfectly painted walls, painted overtop of your old wallpaper.