In addition to the answers you get here, you might want to do some reading on the Furniture forum and the Woodworking forum. I imagine this question comes up frequently on those forums.

You might consider the Formby's build-up remover.

Here is a link that might be useful: Formby's

I've had success with hand-me-down or curb-shopped furniture using "Royal Guardsman" polish. This stuff goes on with a rag, then wipe off. I have found it in my local grocery store. Good luck!

I ended up using the Formby's just because it was readily available at my local hardware store. It is a mild solvent and, with a little rubbing, cut through the few sticky spots and made the wood really clean. I followed it with a lemon oil rub and my dining set just gleams! Now on to re-doing the seat cushions!