Dave - Yes, there are a standard number of dominoes in each set. Sets are defined by the largest doubles with standard sets being double 6s, 9s, 12s, and 15s. Each set has 1 of every possible domino combination (don't forget the zeros): 0-1, 0-2, 0-3, etc.
The basic DOUBLE SIX set has 28 dominoes.
Double 9s have 55 dominoes.
Double 12s have 91 dominoes.
Double 15s have 136 dominoes.

Hope this helps!