It depends on the kind of vitamins. Water soluble vitamins like vitamin c are hard to overdose on, and even then have limited effects.
Fat soluble vitamins such as A and D, on the other hand, are stored in the fat and liver of a person, and can therefore build up to toxic levels over time if you over use vitamin supplements containing these vitamins.
Having toxic levels of vitamins is referred to as "vitamin poisoning", and the symptoms of vitamin A poisoning are quite serious ranging from skin discoloration, liver problems and birth defects.
For more information on vitamins/vitamin poisoning, see: