Ian Stead does some amazing work with planet design, and then puts out the standard Traveller flat map format as well. He uses Cosmic Pack III, which is from a British company called Digital Heavens. It is an artist’s tool that works with Adobe Photoshop to give you cloud overlays and surface templates. It produces beautiful planet images, but they are only two dimensional and cannot rotate. If you don’t want to spend that money, there is a pretty good tutorial on creating planets in Photoshop without the Cosmic Pack plug-ins.
Now, if you have a flat map of your world, and you want to map it to a sphere and rotate it in animation, the answer seems to be Adobe After Effects, and the command “cc sphere.” Seems pretty easy, but you need to have a convincing map of your world with textures. For more information on how to prepare for that metamorphosis, check out this Learning Space article on a flat map of a spherical world. There is another helpful explanation at Introduction to Spatial Coordinates, which is in the help files for the 2008 Microsoft SQL Server of all places! The great news? There is a large collection of flat maps like this at the flatplanet map catalogue.
If you want to go one step beyond, there is a 3d space simulator called Celestia with a lot of add-ons at The Celestia Motherlode. I used the original version of this years ago and enjoyed it then, but as far as I know, it only uses data of known space. I haven’t seen it hacked to portray a fantasy system yet, though I’d love to see it done!