Right now, a lot of people want nightly (and [Rust 2018]) for NLL. It makes the borrowchecking system a lot more precise and less conservative, which in turn makes the language much less annoying to use.

Using nightly as the compiler is much easier in Rust than, for example, using Python 3 early on was, because unlike, say, Python 3, nightly is fully backwards-compatible to earlier stable releases. (While not being backwards-compatible to previous nightlies.)

This means it's easy to limit yourself to the features used in stable + one major change you want, and if there is no change to that major feature, you won't even notice all the instability of the compiler.

There has been some hope of people moving to stable versions as NLL hits them, I think most people will always want the next big feature (personally waiting for const generics) on nightly, at least until the language is a lot more complete.