It depends on the reaction.

For SN1 reactions, protic solvents are better (water).
For SN2 reactions, aprotic solvents are better (acetone).

In real life however, you have to take into account the solubility of your reactants.

There's a common undergraduate lab where students test the reaction rate of tert-butyl chloride with water under different solvent conditions (55:45 acetone-water, 60:40, 65:35, and 70:30). As I recall, it's one of the middle ones that reacts the fastest. You need some water, but you don't want too much as t-butylchloride is insoluble. See the link below for more details. It's under Exp. B - Solvents:

http://www.mendelset.com/articles/690/nucleophilic-substitution-alkyl-ha...