For over a decade I've used hushmail's aliasing feature which allows you to create such custom emails (e.g. [email protected]) on the fly almost instantaneously. I use one per service that requires an email to sign up. Works great.

You can do it with the free account, too.

Just delete one if you are obviously getting spam because of a service selling their email lists. Which is a reality for "free" services. Bonus points because you can identify exactly who it is that is doing this and have the option of publicly shaming them.