In most cases, yes. It’s usually possible to recover files you've accidentally deleted from the Recycle Bin in Windows (or Trash on a Mac).

When you empty the Recycle Bin, the files aren't really deleted just yet. They still reside on your hard drive, but you have a limited window -- maybe a few days or weeks -- in which to recover them. If you wait too long, your operating system will write over this reserved space with new data.

The more free hard drive space you have, the more likely your files will still be accessible. Avoid doing anything major with your hard drive (such as use the disk defrag tool) until you've recovered your data.

To "undelete" these files, you'll need to download third-party software. (Programs that can recover deleted files aren’t built into Windows or Mac OS.) "Data recovery software," as it's usually called, will allow you to preview deleted files so you can choose which ones to recover.

Popular solutions for Windows include Recuva, Uneraser, Undelete Plus, Data Recovery Wizard and Restoration. Mac users might consider Data Rescue 3. Some programs are free (such as Recuva), while others allow you to view your deleted files for free but then ask you to pay a few dollars to recover them.