Is it worthwhile to replace the hard drive in a 24" 2008 dual core intel iMac?

If you still have a use for it it's definately worth it. You can upgrade the ram to a maximum of 6GB and run the current Yosemite OS. Hard drives are cheap and it's not that difficult, here's a step by step guide https://www.ifixit.com/Guide/iMac+Intel+24-Inch+EMC+2134+and+2211+Hard+Drive+Rep lacement/8968

I replaced my hard drive in my 2008 Intel duo core Macbook pro and put in a solid state drive, its like getting a new machine, definitely worth it.