My computer does not have enough memory to back my phone up but a few times it has tried to back its self up and now I barely have any memory. Any idea how to get rid of those backed up files? It's a few GBs of memory gone.

Depending upon what type of computer you have, the location of the files varies.A quick Google search on iTunes backup locations would have given you this Apple link: http://support.apple.com/kb/HT4946 which answers your question.

Backing up an iPhone never takes 32GB of memory... it really should not take more than 1 or 2GB at the most. NO media is included in the backup.

Remove the incomplete backups if they are what is really taking up space.

Where iTunes backups are stored on your computer

The folder where your backup data are stored varies depending on the computer's operating system. Make sure the backup folder is included in your periodic data-backup routine.

iTunes places the backup files in the following places:

• Mac: ~/Library/Application Support/MobileSync/Backup/
• Windows XP: \Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\
  Note: To quickly access the Application Data folder, click Start, and choose Run. Type %appdata% and click OK.
• Windows Vista and Windows 7: \Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\
  Note: To quickly access the AppData folder, click Start. In the search bar, type %appdata% and press the Return key.

It also might be time to consider a larger hard drive or moving the media to an external drive.