When I release a project, I start at 0.01, then release 0.02, and so on. The version numbers mean nothing to me, other than that they are increasing.
I still have people email me, though, and say things like, "I saw your project Foo::Bar, when do you think it will be 1.0?" I don't really know what to say...
Some applications have their own numbering conventions to indicate what kind of an update a new version is. If you're familiar with the software, it's useful to know at a glance what to expect. (The Linux kernel and gcc do this.)
You can ignore this convention, but you're going to encounter confusion from potential users.
It's moronic to compare version numbers across products precisely because standards vary so widely. I'd say that Django 0.97 was more stable than Rails 2.0, yet it's not even a 1.0!