Yes. There is software that can scan the drive and recover deleted files. You'll have to google around for it, as I forget the name of some I used to have. What these programs will do is recover most of the files but they may or may not be without original names so you'll have some reordering and sorting to do when it's done.
If they're irreplacable and you have some money you can send it to a recovery service like drivesavers.com (or its competitors). These services can often recover a lot of data for a few hundred bucks (they can even do it from drives that have mechanical failures but that goes into the thousands).
In the mean time avoid using that drive for any reason and certainly don't put any new files on it. Any write operation to the drive may be overwriting otherwise recoverable data causing you to lose the ability to be able to recover what you want.
None of these methods is 100% but can be pretty close. Of course if you continue using the drive prior to attempting recovery you'll get less and less out of it as sectors containing key pieces of files get overwritten.
So unplug that drive, research the solutions for software and/or sending the drive in. If you go DIY I would practice using the program on a flash drive first so you understand the options and how it works. You'll probably need a second external drive since you won't want the destination drive for the files to be the same as the source (this isn't as simple as just undeleting so you can't put recovered files onto the same drive its recovering from).
If these are really important to you like irreplacable photos then don't screw around and just mail it in or take it into a professional service. You'll be more glad you have those baby or family photos 10 years from now than having saved the extra $250 or whatever it would've taken to recover them.
