Hi ZenShakti,
I’m guessing you mean a mattress protector (vs a mattress cover which is part of the mattress itself).
I would certainly recommend a mattress protector to protect your mattress from the normal body fluids and oils that we all release each night and to guard against stains from spills or accidents which can void a warranty and also to keep your sleeping surface in a clean and hygienic condition.
There are different types of protectors and which one is best depends on your circumstances and the criteria that are most important to you (including cost) and post #89 here (and the posts it links to) has more information about the tradeoffs involved with different types of mattress protectors and links to some good sources for each of them.
Phoenix