Bunches of questions here
1. Does it happen in different front chain rings?
2. Does it happen in different gears on the rear cassette?
3. What type of shape is the cassette in?
4. What type/brand of shifters?
5. How new/old are the cables?
6. How new/old is the chain? Have you checked it for stretch?
7. Is the chain dirty or clean?
8. How clean/dirty are the cables and housings? (as Faith asked) Does the cable slide in the housing easily?
9. Have you tried the barrel adjuster on the rear derailleur? Can you see the rear derailleur physically move when you adjust it?

Basically clean and lube everything in your drivetrain. That will take care of many issues.
Make sure your shifters are adjusted correctly or take your ride the your local bike shop.
Replace (or have replaced via the LBS, again) each part in the drivetrain. Typically start with chain/cassette. That will solve 90%.