Is it possible to mod an N64 controller to connect to a computer?

There are at least two ways of doing this, one easy way and one hard way.

The easy way:
Buy a USB Adapter. Although these have been discontinued, there might be some similar products on Ebay (Included a Ebay link with similar products).

The hard way (Do it yourself way):
Making a PIC board, which can support it. A reasonable tutorial to doing this can be found here.

You can buy a USB N64 controller ($10 on ebay - link removed: see below).

Edit:

Don't buy them. I've bought many of these cheap N64 USB controllers, all from different sellers, and they're all crap. The analog always maps to the same controls as the D-pad, and isn't even true analog. I've had this even when the listing describes the controllers as having "true 3D analog" or some other crap. Buy at your own risk.

Instead I'd recommend modding your existing controllers, or just buying expensive USB ones from a reputable brand. If you do get stuck with a dysfunctional fake controller from ebay, file a dispute right away.