Ichthammol - not sure if a pharmacy near you carries it, but it's excellent to have on hand. It's a black drawing salve, and you put a little over the splinter (a piece of the splinter should be exposed, or the skin over it should be open slightly), then cover with a bandaid. It will draw the splinter out.

It's also excellent for bites/stings.

Edit: (It's pronounced Ick' thu mall)