I cut grapes for my 13 month old, but not for my 3 year olds. They have their full set of baby teeth and have no problem chewing a whole grape (although they do tend to eat them in bites rather than all at once). Anyone can choke on a grape, not just children. I always supervise their meals and I know how to perform the Heimlich on children, if it is ever necessary.
My 3 year olds freak out if I try to cut the grapes, anyway. They even want them still attached to the stem, so they can pick them off.