If you use a disposable email address on your site, you can disable it as soon as spammers have discovered it. Of course, you have to give every welcome contact their own alias (or your real email address) so they can continue to send you mail even if you disable the alias they originally used to contact you. Fortunately, this can be as simple as using the new address in the Reply-To: header.
Some disposable email address services also allow you to set up a white list of senders that are always allowed to send you mail at any disposable email address. This has the small disadvantage that spammers might by chance or by whatever other means guess such address and get through with their spam, though.
Alternatively, you could use aliases that automatically expire. If a new disposable email address appears on the site every day, for example, they all could be set to expire after a week or so.
Use Disposable Email Addresses, Eliminate Spam
Either way offers a relatively simple, but very effective weapon against spam. If you are consistently and exclusively using disposable email addresses on web forms, in forums, on Usenet and in discussion groups, with your contacts and on your own Web site, I believe you can curb down spam to an absolute minimum.