We've recently deployed a system that is much more comprehensive than a simple IP block. It's fed from actions that users and moderators take, and the data is shared across the network. This means, folks rejecting spam edits on Stack Overflow are also helping to keep DBA, Skeptics and Seasoned Advice a cleaner place.
In the case of edits, if a user spams them more than once or twice on any site, they'll quickly find themselves unable to make them any longer. If that user is anonymous and tries to spam a post that has a history of being a spam target, they're pretty much instantly blocked.
There are two related posts (note, two links) about this on MSO - and we're not yet done refining the system. We will still see a little bit of spam in suggested edits (well, enough for humans to be able to identify it once) - but the system does a very good job of keeping it out afterward.
In short, just reject the edits as spam, flag spam as such when you see it. For moderators, it's important that you destroy obvious spammers on sight, this is all signal that we collect to know what to keep out. I can't go into specifics of how the system works, but I will say that it works on more than just individual IP addresses, and has an extremely low false positive rate.
The automatic, but more basic defense built into suggested edits is still there (as Aaron pointed out), but the new system (code named Spam Ram) generally kicks in before that does, since it has history from the entire network to draw from.
There's also a related help center article in place for folks unfortunate enough to get caught in the cross fire, but that happens rather rarely.