Different servos draw different amounts of current. And the amount of current they draw depends on whether they're starting from a standstill and how much friction the servo arm is encounter.
The max current the servo will draw is encountered when the arm of the servo cannot move. That is called the stall current.
I don't have a list of stall currents for servos, but here are scopes of peak currents for several different types of servos:
The ones with the lowest peak currents are micro or sub-micro servos. The highest ones are larger servos. These peak current tests are based on making small movements... which is like starting from a standstill repeatedly. So your power supply should probably be able to supply at least this much.
I'm running two sub-micro servos in my project and based on these tests I decided to use a power supply capable of delivering 1.5A, just to be safe.