How to clear unwanted files from Time Machine backups
If you have a file or two you wish to remove from your Time Machine backups, you can do so right in the Time Machine interface.
Apple's Time Machine feature is a full-system backup routine that will maintain hourly backups for the past day, daily backups for the past week, and weekly backups for as long as there is space in the drive to store them, and uses a feature called "hard linking" to share unchanged data of previous backup files with new files copied to the backups. This routine should ensure that even with a relatively small backup drive (at least the size of the collective data you are backing up), you will have ample system restore points and access to prior versions of files. In this way, Time Machine can maintain extensive snapshots of your system over time.
However, backing up large data sets reduces the number of backups a smaller drive can hold, so if you want to keep more Time Machine backups available, you don't want to keep backing up large and unnecessary files, such as a copy of a movie you don't plan to watch again.
Other examples of such files might be a virtual-machine image for programs like VMWare Fusion or Parallels Desktop, which can sometimes be many gigabytes in size, or large downloads you may have removed but that got backed up. (To save space on the Time Machine drive, I recommend excluding the Downloads folder in your home directory from the Time Machine backup routine.)
Even if you exclude a file from Time Machine, prior backups of it will still remain until new ones push them out of the Time Machine drive.
Instead of deleting the file from each backup manually, you can remove all instances of it immediately from Time Machine if you wish. To do this, simply go to the file's location and invoke the Time Machine interface (done from the Time Machine menu). When the star-field view of Time Machine appears, locate the file in the foremost window, right-click it, and choose the option to "Delete All Backups of [filename]" and confirm the action.