Peeling and Fading
As mentioned before, wallpaper doesn't last forever and will eventually start to peel off. If it doesn't begin to peel, it will most likely suffer light damage that causes the colors to fade and become dull over time. For rooms that have windows that give in a ton of sunlight, this is a large problem. Although it is not necessary to immediately replace your wallpaper if it starts to peel in a few places, which can be a good sign to start to watch it because it will gradually become worse and worse. Most guests will not notice it if it is just a small amount of wallpaper peeling here and there, but if you let the problem continue it will definitely become noticeable.
Once your wallpaper has peeled for awhile and is starting to remove itself from the wall, you will know that you need to put up new wallpaper. Also, if the colors have just become a part of the room and aren't really noticeable, then your wallpaper is no longer doing its job and has faded to a dull, boring color. Fading is sometimes hard to notice because it happens so slowly, so it helps to be consciously aware of the fact that it is indeed fading.
Change in Decoration
It is not uncommon for somebody to get bored of the same old furniture and decoration, but with a change in decoration comes the need for a change in wallpaper. Wallpaper is typically chosen to match the color and design that a room's furniture and decorations have, but if they change then the wallpaper will no longer match. Unfortunately, you will have to go through the tiresome process of taking down all your old wallpaper and replacing it, or you could always go with the option of just using paint.
Your wallpaper not only needs to match in color, but unlike paint, the patterns are very important as well. Painting usually leaves a solid color, but wallpaper comes in various designs and shades. Your old wallpaper may no longer have the right style, even if the colors still match. If the style is wrong you will still need to replace it otherwise it may look tacky.
After Buying a New Home
If you just moved into a new home, you should always replace the wallpaper just in case the previous owner was a smoker or had pets. Smoking leaves behind an odor that the wallpaper absorbs that will make your new home stink, while pets will leave behind a stinky odor that often makes the home smell like you own cats, or it can even smell like urine if the pets weren't completely potty-trained.
The only exception to replacing your wallpaper after buying a new home is if the previous owner specifically says that they replaced the wallpaper right before selling the home. For more expensive homes this is not uncommon as it allows them to sell the home for more profit, as well as having the advantage of being able to sell it much faster.
These are the main reasons why you would need to replace your wallpaper. There may be a few other reasons why you would need to replace it, but that would happen on a situation-to-situation basis. Replacing your wallpaper may be difficult and stressful, but it will make your home look much better afterwards. It is worth the extra work and cost.