Yes, quite simple actually. Pull the hard drive, hook it up with a SATA to USB adapter to another computer, and copy any data you need from the drive. You could also install the drive in an external USB case and keep it as a backup drive.
If you have a desktop you do not even need the adapter, you can just power off desktop, connect a sata data cable and a power cable to the drive, repower computer and you should be able to access the drive (dont remove your original hard drive as you still need to boot from that hard drive).
Otherwise you can do as itpro said and get a usb-sata adapter or a 2.5" external enclosure.