I've had an external hard drive for years. I rarely use it. I keep all of my old photos on it. Tonight, I was transferring photos from my old computer to my hard drive so that I wouldn't lose them. It worked for a while, then all of a sudden, when I plugged it in, it started making a clicking noise, and the computer wouldn't recognize it as being plugged in. What can I do to recover those files and put them on my new computer?
Check the usb cable to see if it is correctly linked, try it on another computer, change the connecting cable, if all these do not work maybe you will need a data recovery software
this is a free version and you will be able to recover 1GB files. After the installation, firstly link your HD to the pc, secondly click deep scan. Wait till the scanning is over and then preview the files need to be recovered. And save them in another place.
If the software still cannot help you then you may have to send your HD for repair.
Just out of curiosity what brand is the HDD (Western Digital, Seagate, etc.)?
dasgore is right - you will need to attempt recovery. The clicking sound is a bad sign and normally indicates hard drive failure.