|Syntactic Confectionery Delight|
Ignoring backwards compatibility isn't really an option, IMO. I like this post by Alias on that particular subject.
One way to add new features but ensure back-compat is to have a comprehensive test suite. We've tried very hard with the Catalyst project to have a sufficient test suite so as to make sure that any piece that gets changed doesn't affect the expected behavior.
Sometimes you can't help but break back-compat. In cases like that, you could probably do that under a major revision increment (1.x -> 2.x). That way people might be able to understand the api breakage.
I wish CPAN worked a little differently. Currently if you release 2.x of module, then 1.x is basically dead. This doesn't give your users the option to keep their app stable with the 1.x releases while getting security/bug fixes. Either they switch to 2.x or they're left in the lurch. You can still release a new 1.x version, but it just means that people have to install it manually. Ah well.
Just thought that i might also mention dev releases. In order to smooth over the transition, you could release a series of 1.99_0X dev releases where your bleeding-edge users can try out the new api and prepare for the upcoming 2.x release.