I've got a bunch of film cameras plus some digicams. But I do think there's something to be said for shooting with very primitive gear. I've taken some good shots on my Holga 120N (at least other people think they're good, and I even like a few). Last week I received my own plastic "Debonair" camera being sold by the Film Photography Project. It's basically a chintzy cross between a Holga and a Diana, and shoot 120 film in 6x4.5 frames. I took it out for a few spin last weekend and had a blast. The controls are incredibly basic, the plastic lens is a "prime" 60mm or so. Aside from focusing with the 1-person, group of people or "mountain" options, it's pretty much point-and-click.
I think what's freeing is that (1) I keep my expectations for things like sharpness low and, (2) I'm freed from worrying about mechanical details so I can give the subject more of my attention. I'm not saying you can't do the same with any camera (it is a mindset, as we all know), but the lack of distractions tends to make it easier to focus on the subject instead of wondering if I should use a different lens, how much DOF do I want, etc.