Is it a hardware or software issue ?
With no program in your device ( blank memory ) does the servo still attempt to move when you power up ? If yes, then there is a hardware issue and ladyada's suggestion about pullup/pulldown resistors to hold logic state inputs to avoid the effects of logic state transistions during the power up (or down) moments is what to do. Adding such resistors anyways is a good idea for servo command and enable control lines.
If it did not move, then it may be your program. Whether it is the program causing the unintentional movements or not, have some delay timer at the beginning of your program (like 10 seconds) to allow all of the hardware to power up and settle down.
Depending on your design intention, then the program or user can initiate a 'homing' sequence and operation.