The car is a 96 Legacy 2.2 auto 100k.  I recently replaced the steering rack, ball joints and control arms and the sound started happening about 500 miles after. I'm hearing a brief squeak or squeal coming from the front of the car when blipping the accelerator when driving, its also present when hitting a bump. Its also easily produced when turning and accelerating at the same time. It won't make the sound in park, but not moving the shifter from park to reverse will usually produced the sound.  Braking doesn't effect the sound and since the car makes the sound when parked as well I'm ruling out brakes. While the car is parked i've tried to reproduce the sound by rocking the car back and forth, nada. Also tried shaking the engine by hand to check the motor mounts.  I tightened the AC and accessory belts, didn't change anything.  Any help is appreciated cracking the mystery of 1000 squeaks.

Chock the wheels, set the parking brake tight, put up the front of the car on jack stands, and have someone shift from park to reverse while you listen for the noise under the hood and under the car.

Likely to be either exhaust mount bracket/hanger, or a loose transmission or motor mount. Don't forget to check the dogbone mount on top behind the throttle body.

I have had scurrying noises for quite a while when I turn the engine on; I don't know whether it is little animals like mice or actually the water flowing through the dashboard area and out.....

check the crank pulley for wobble. If the inegritiy of the rubber in the 2 piece crank pulley degrades enough, it can even sping, throw belts and other wise act up. Some folks say to use a permanent marker or grease pencil to draw a line across the pulley, then check that it's lined-up after a drive.

 

The car can also be briefly run with the accessory belts off. If no squeak, then it could be an accessory's pulley????

I had similar symptoms on a recently purchased 05 OBW.  Turned out to be a transmission mount.  lstevens told me to jack up the front end - stick a pry bar between the transmission and the transmission mount and flex it.  That reproduced the 'squeak' and I could see the torn rubber.  He stopped over the house yesterday and we swapped it out...much easier than I thought.  Thanks lstevens, problem solved!

problem solved. While checking the transmission mount, i found that the exhaust hanger that connects to the tranny had snapped.