Following affiliate clicks - possible?

I'm not 100% sure if this can be done, so please bear with me:

I have a site where users register. On the site I promote several affiliate links.
Is it possible to tell which registered user clicked on the link and made a purchase?

The only way I can think is to present different sub ID affiliate links to each user, but I was kind of hoping there will be an easier answer?

Can any of you guys think of a solution, maybe even a script that can take care of this sort of thing?

Thanks in advance.

Poster :