As someone who doesn't typically have reason to use either -- is using floats rather than doubles actually common? I was under the impression this was pretty rare.
It's not rare at all. A double takes up twice as much memory as a float and memory bandwidth is a precious commodity these days. If you have a lot of numbers (e.g. in 3D models or similar) and don't need the extra precision, using floats is an obvious choice.
Most video games use floats. This is because doubles will be emulated in software on some platforms, thus making them incredibly slow. The Unreal Engine, for example uses floats extensively.
Also, most modern x86 processors can perform single-precision operations twice as fast as double-precision, which helps (and saving memory bandwidth is good too.)
On PPC/ARM, single-precision allows you to use Altivec/NEON, which can give significant performance boosts as well.