Isopropyl alcohol is generally what is used during PCB assembly to remove flux residue. It's pretty safe, and it's good at removing all sorts of nasties, including conductive dust/dirt, and it can take off some corrosion with a little (light) scrubbing. Just make sure you let things COMPLETELY dry before you hook it back up. Remember that alcohols are very flammable, and some might get underneath a chip, resulting in drying times longer than you'd expect. I suggest letting things dry overnight.
You can also put the thing in the dishwasher. Remove all socketed chips, and put it on the top rack with no detergent. Don't do this at the same time as a load of dishes

Use a rinse and hold setting as the drying heat can be a little hot. Just let it air dry for few days. I'd suggest rinsing it down first to get rid of any excessive buildup, and I'd also recommend a cycle afterwards with nothing in the washer just to remove any stray contaminants that may remain (there shouldn't be any, but why chance it).
I prefer alcohol myself. Several have reported good luck with a dishwasher, though. Some are concerned with lead contamination in the dishwasher, but I really don't think that's likely to be an issue given the volumes of water involved. I think some of the other chemicals used in the solder fluxes are likely worse, but still not likely to be a problem. If you'd rather not chance it, don't, though. If you happen to have an old dishwasher going unused, give it a shot!
