You can. Now, having said that, it's not like just plugging into the USB/PS2 port.
The heart of the optical mouse is an ADNS chip from Agilent/Avago. Aside from a couple chips from ST Micro, Avago is the only manufacturer of this kind of chip.
To keep it simple, the interface between your microcontroller and the ADNS chip (depending on the model) is either a dual Quadrature interface or a simplex/duplex serial interface, or both. With the quadrature interface, you can get the DeltaX and DeltaY values. With the serial interface, you can pull position information, framegrabs from the sensor itself, monitor surface quality, and more.
Here's the ADNS-2610 datasheet.I'm working on building my own carrier board for a similar chip (ADNS-2051) with a customized optical lens system so that I can place the sensor more than 2.5mm from the ground and use it instead of wheel encoders for positioning.