(This is a bit long winded, but I believe my explanation is sufficient to answer most questions related to this; if you just want the answer with no explanation of what the implications of doing this are, read the first paragraph)
This is a bit old, but to help others out..
TrueCrypt, at least with version 7.1, has an option to do "in-place encryption" on a non-system drive or partition (also a system drive or partition, but let's just talk about the non-system). What this means is that the files that are currently on the hard drive will be encrypted without having to be moved. Note that in-place encryption, at least for the Windows version, requires that the target files be on an NTFS partition; FAT will not work. As always, it is good practice to backup any data that you do not want to lose before doing this. Also note that this will not encrypt older files that have been deleted from the file system, only current files (deleting a file, even from the recycle bin/trash can does not completely erase it from a hard drive).
After the TrueCrypt volume has been setup, any files that are created in the volume will be encrypted "on-the-fly". Keep in mind that if you are working on, for example, a word processor document, and you save it to an area that is not part of a TrueCrypt volume before moving it, then there will be a remnant of that document on your hard drive. You should also be aware that some applications auto-save your progress for the purpose of file recovery in the event of some sort of crash, or simply for convenience. This means that the data in this hypothetical document you're working on will likely be stored in some other, possibly unprotected area, most likely in the form of application cache or temporary files.
All this being said, if you absolutely* (nothing is absolute, but this is very close) want to ensure there are no data remnants on a hard drive, you should setup a TrueCrypt volume on the entire drive when it is brand new. If you only care about certain files, and have more than one hard drive, you could use one as a sort of "scratch pad", and move files to a TrueCrypt volume on another drive. That way the TrueCrypt drive will not have any of the application cache, temporary files, etc. associated with the files, just the encrypted version.
Although I have discussed a number of gotchas with encryption, it is good to remember that transferring an encrypted file to another storage location, assuming you are using a good algorithm, is still secure. I was just trying to emphasize that encrypting a file that was worked on or stored unencrypted on a hard drive and encrypting it on that same drive will not guarantee that it can't be recovered. It is also useful to remember that I am talking in absolutes here. Will encrypting your files prevent a relative from looking at them? Yes, unless your relative knows how to perform data recovery. Will encrypting them stop dedicated cybercriminals from reading them? The encrypted versions yes (assuming a good algorithm, etc.) but the data stored elsewhere on the drive? No. Of course, there are a lot of people who don't really do anything that would put sensitive information on their computer, and if they do, the information usually isn't THAT important. If you have private information on your computer, but the world won't end if some dedicated data forensics expert decides they want it, then encrypting in-place is probably fine. When it comes time to get rid of the drive, assuming it is still operational, writing random bits to the drive will most likely prevent the most common data recovery methods from retrieving any data. If you've got a hard drive that used to have all your passwords, credit card numbers, social security numbers, etc. written down inside a text file, then the drive needs to be destroyed, as a dedicated cybercriminal with a lab environment might be able to recover that data.