The hard drive was failing so I decided to upgrade to an SSD.
The installation was pretty easy, but required some additional parts to keep the machine happy.
For replacing a hard drive with an SSD, an adapter bracket needs to be used, in addition to a third party thermal sensor to keep the fans from running on high all the time after installation (as the original hard drive contains an Apple sensor that the iMac expects to be present).
Make sure to have already created a bootable OS X installation disk or be able to boot to the recovery partition on the original drive using an external adapter. iMacs prior to 2011 do not have Internet recovery and will be unable to boot unless an installation media is present.