Mineral spirits have worked for me. You might also try nail polish remover (which most people are more likely to have on hand).
This depends upon if it is latex or alkyd. Steve has the alkyd covered. For latex (water based) try Dawn Power Dissolver or Simple Green.
You can also go the The Depot and get a product 'Goof Off' that works on most paints.
My steam mop removed old paint splatters off wood floors. Sure it would work even better on tile