CDs usually skip because of small scratches on the surface. (Some CD players are far better at handling scratched CDs than others, so while it might seem that one CD player never skips whereas another one often does, it's still a problem with scratches that really needs to be addressed).
It's probably time to reach for the Brasso (or for a 'whitening' toothpaste, which also works well):
http://www.instructables.com/id/Re-surfacing-CDs-so-they-work-again./
[NB: When cleaning CDs, always use 'in and out' motions and NOT 'round and round' ones]
However, in order to give the CD player the best possible chance of ignoring any minor scratches (which might be almost undetectable to the naked eye), it might be worth trying a lens cleaning disc. They're available cheaply in many 'discount' stores and, of course, online:
Amazon.co.uk User Recommendation