Can I connect servos directly to the uno?

Can i use 2 separate battery packs.
Can i connect the servo power wires and the sharp IR power wires to a breadboard and then use a voltage regulator and a battery pack to power these.And then use something like this Arduino Playground - 9VBatteryAdapter and a separate battery pack to power the arduino.I wont have to use antoher regulator as the arduino already has one on board correct??
But do i have to connect the ground from the regulator on the breadboard to the ground on the arduino??? or the ground from the servos and sharp IR to the breadboard gnd and only the signal wires on the arduino??