OFF (Object File Format) is about as small as a mesh format gets - a header, a count of vertices and faces, then the numbers. It turns up mostly in academic geometry work and mesh-processing datasets, where being trivial to parse matters more than being widely supported.
Every conversion below runs in this page, on your own machine. Nothing is uploaded, there is no queue, and there is no account to make. Pick a target format, or just drop an OFF file above and choose afterwards.