Some games will install themselves partially, if not fully to disk and only require the physical BR/DVD for validation. Stuff installed over PSN/XBL digital download will obviously reside completely on the HDD.
Put in an SSD!
Much faster load times.
For PS3 it's easier because the device will accept any standard hard drive, just be sure the firmware does its own garbage collection because the OS likely doesn't support TRIM.
I dunno about current Xbox360 firmware, but on older versions third party drives were enabled by writing to the MBR to make it appear as if it were an official Xbox expansion drive.