If yours walls are painted with a glossy or eggshell finish, smudge marks and fingerprints usually come off easily. It's a different story if the paint is flat; without the resins that create sheen, flat paint absorbs stains. And if you try to rub them out, you can easily wear through the paint. A combination of soap and clear water works best, but test it first. It may create more problems than you already had.
Try Plain Water
The safest approach is to start with the mildest cleaner, which is plain water, but it might not work on a flat finish. Weak cleaners must be coupled with a certain amount of rubbing action to be effective, and rubbing flat paint is a quick way to damage it. If the finish has any gloss, though, rub it lightly with plain water, and if that has no effect, mix a solution consisting of 1 ounce of dish detergent per gallon of warm water and try that. The detergent may have just enough emulsifying power to handle the smudges.
Washing Flat Paint
The best approach to take with a wall with a flat finish is to wash all of it with soapy water and then rinse with plain water -- the finish is too fragile to spot-clean. Mix a solution of 1 or 2 ounces of dish detergent per gallon of warm water; soak a rag with it, and, starting at the top of the wall, wipe the entire surface gently. When you're done, repeat the procedure with plain water; then dry the wall by lightly wiping with a dry cloth. Wipe as gently as possible, avoiding strong abrasive action.
Washing Glossy Paint
If your walls have any gloss at all, you can try stronger cleaners to remove problem smudges and marks. If the soap solution has no effect, mix a solution consisting of 1 cup ammonia, 1/2-cup vinegar, 1/4-cup baking soda and 1 gallon of water. Try this solution on an inconspicuous part of the wall, and if it doesn't affect the finish, use it to wash off stubborn marks, wiping lightly with a non-abrasive cellulose sponge. A paste made with baking soda and water, rubbed gently onto the most stubborn stains with the sponge and rinsed off, should remove the stains.
Fingerprints and smudge marks tend to build up, and washing lightly before they become noticeable is preferable to trying to erase them when you can no longer ignore them. Once things have gotten to that point on flat paint, your best option may be to repaint, especially if the marks are on flat paint. If the walls have a gloss, you can also remove marks with a 1-to-1 solution of vinegar and water, which is also good for removing smudges from woodwork and trim that have been painted with enamel.