It's too late to remove files. All you can try at this point is to clone your drive to a freshly erased external drive. You will need your installer DVD for this:
Booting From An OS X Installer Disc
1. Insert OS X Installer Disc into the optical drive.
2. Restart the computer.
3. Immediately after the chime press and hold down the "C" key.
4. Release the key when the spinning gear below the dark gray Apple
logo appears.
5. Wait for installer to finish loading.
After the installer finishes loading, select your language and click on the Continue button. Wait for the menubar to appear at the top of the screen.
1. Open Disk Utility from the Utilities menu.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Select the destination volume from the left side list and drag
it to the Destination entry field.
5. Select the source volume from the left side list and drag it to
the Source entry field.
6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
No guarantee you will be able to do the above, but at least give it a try.
When the drive is too full your only recourse is to reformat the drive. I'm afraid you will lose everything that is not backed up already. You may be able to recover some files using special software:
General File Recovery
If you stop using the drive it's possible to recover deleted files that have not been overwritten by using recovery software such as MAC Data Recovery, Data Rescue II, File Salvage or TechTool Pro. Each of the preceding come on bootable CDs to enable usage without risk of writing more data to the hard drive. Two free alternatives are Disk Drill and TestDisk. Look for them and demos at MacUpdate or CNET Downloads. Recovery software usually provide trial versions that enable you to determine if the software would help before actually paying for it. Beyond this or if the drive has completely failed, then you would need to send the drive to a recovery service which is very expensive.
The longer the hard drive remains in use and data are written to it, the greater the risk your deleted files will be overwritten.
Also visit The XLab FAQs and read the FAQ on Data Recovery.