Below is a video of a gamer installing a old 20GB HDD from their old Xbox 360 into their Xbox 360 Slim. It may take some patience as there is not enough finger room to help you guide the HDD. You'll have to "drop" it in and hope that it lands on the SATA connector ports inside the Slim.

The other hardest part is removing it from the Xbox 360 Slim as there is no way to grip the HDD with your fingers. In the video, it shows that pliers were used (not recommended). I'm sure you will (or someone) will come up with a better way. Kind of like a pull tab with tape? (you heard it hear first as a suggestion!)

Its been confirmed by others that not only the 20GB works but the 60GB, 120GB, all the way up to 250GB. But take a look at the video and see for yourself.

*Note: Performing this may void your warranty. Perform at your own risk.