Iowa State offers an exceptional NEXRAD composite image as GeoTIFF for the entire continental US at a reasonable resolution. Is there a comparable GeoTIFF composite updated semi-regularly available for the entire world, or at least other major continental areas?
I don't know of any, and I doubt there is a single source. You might be able to build one, but some places (e.g. Australia) simply don't have full coverage.
Another option, if you just want global coverage (which pretty much means satellite) is to look at the NASA MODIS layers. There is a lot of data, going well beyond the "pretty picture" level.