To permanently obliterate a file, you must trash every past residence it has occupied. How thoroughly you trash and how far back you look should depend on just how paranoid you are.

For the mildly concerned, overwriting the file "at least once" may be enough. You might get away with just defragmenting your hard disk, if it's relatively fragmented and relatively full. This is likely to foil the most primitive recovery efforts.

Much more adviseable and barely more difficult is to use a software application designed for file wiping. PGP includes such a tool among its other goodness. (I'll leave encryption as a separate topic; this isn't about general security, just file trashing.) When you "wipe" a file with PGP you are overwriting it with garbage, many times. PGP also includes a convenient option which does this to all free space on your disk. The documentation can tell you more, but essentially you are not only changing all of the stored bits but are also attempting to confuse the natural magnetic memory of the hard disk. This makes recovering your ex-data impossible for commercial products and very difficult/expensive for serious snoops (like TLAs, and other conspiracy interests).

If you're really paranoid you should consider the possibility that, while your file may be a dim memory, information from the file may be entangled elsewhere. Possible locations include crash recovery backups (Microsoft Office is notorious for creating these), your swap file (depending on your operating system), and even as a kind of stress pattern in your RAM. Anyone who cares this much should be doing their research elsewhere, but suffice to say the only sure way to permanently obliterate a file is to physically destroy the computer. Set up thermite or other demolition materials so you can quickly slag all hardware if the secret police come knocking.

Finally, if you're selling a computer or otherwise passing it on intact, basic common sense is to keep the hard drives. Given the pace of industry, the new owner can probably get something better for less. You can easily keep using the disks in your new computer, or you can introduce them to your friends Fire, Acid, and Hammer.