I have a Weller desoldering iron, which has hollow tips, and a vacuum bulb to suck away the solder. I only use it on printed circuit boards, where it works fairly well.
For other jobs, I often use solder wick to soak up excess solder before reconnecting things.
I think Jim's tip to use a toothpick to clear holes is a good one.
Here is a picture of the business end of the desoldering tool, I didn't find a picture of a complete unit.
