Clean the paint as soon as you can. Use a rag dampened with water for water-based paint, or mineral spirits for solvent-based paint. If the paint is still fresh, it will come off easily.
Soak a rag in hot water and hold it over dried water-based paint for a minute or two. The hotter the water, the better -- the combination of heat and water will soften water-based paint. Scrub it gently with a kitchen scrub sponge. If it's a blob or drip, use a plastic scraper, credit card or even your fingernail to scrape away the blob.
Rub the paint with a commercial, solvent-based latex paint remover if the paint is stubborn. Sold in paint and hardware stores, this product will remove old, dried water-based paint but will not harm most cupboard surfaces.
Rub acetone on factory-finished metal or melamine cupboards, turning the rag frequently and adding more acetone as needed. Acetone will remove most types of dried paint but isn't harsh enough to damage most factory finishes. Don't use acetone on varnished wood cupboards because you'll be left with a dull spot. If you don't have acetone handy, use nail-polish remover -- most contain acetone.