Beside using some ico sphere, there is another way to do it. It might work or not depending on the kind of game you are implementing.
Have your classic 2D tilemap with squares. Make it wrappable. That's it if you got to the end left you will come back to the right, etc.. Like Asteroid but make the camera move instead of the player. Navigating through such a space already give a 'sphere impression' because if you keep going in a direction at some point you will come back to your initial position. It's not 100% accurate though because if you go in diagonal the path would be longer than if you go in a straight direction.
Then the trick is to use a spherical vertex shader to make the 2D plane looks like a sphere. The idea is to rotate each point in function of their distance from the center of the screen. There is not much about it on the web but it's not difficult to implement if you know a bit of GLSL.
The nice thing is that all the logic is very simple because it's still 2D however it gives to the player the illusion that he is playing on a sphere. Here is a proof of concept (a project that I sadly abandoned) :