I've had several HD's die on me during the years, sometimes the disc wouldn't spin at all, and sometimes spinning but making those clicking noises. Last time I had one die on me was a Maxtor One Touch drive that died because of overheating (my best guess anyway). A friend of mine recommended a program called Stellar Phoenix Recovery Suite and gave me his copy for loan, sure enough, I managed to salvage almost everything from the drive, with just few gigs unsalvageable out of the 300 or so that it had.
When I did that, I knew of the risks involved and that there'd be a chance that the data is forever lost if I meddled with it myself and something went wrong, yet I ended up doing it. The clicking isn't always about the chip going bad like Chris said earlier, but it could very well be signs of it doing so and that way I'd strongly recommend not using the same drive again at all. The recovery process with that program took almost one full day with next to no user input required beyond the initial selection of things to restore along with selecting where to restore them.
Also, if there's no clicking sounds but the drive is still not seen by the operating system, you can try to reactivate it from the administrative tools in Windows by going to the disc management and re-enabling the disc. It's also possible that the start sector has gone bad and that way the actual data is still there available for restoring.
Basically in the end it all boils down to whether you're prepared to take the risk of ruining the disc and the contents entirely by trying to recover it all by yourself, or if you're ready to dish out the cash to have professionals do it for you, which is nearly guaranteed success in most normal cases.