When a cylinder is added to a scene Triangle Fan fill type for the cap is provided in the last operator panel.
Is there any tool to use with a circle to fill it like triangle fan would do?
The alternatives Grid Fill and F (n-gon) can't be used when the vertex in the center of the circle is required.
You can do this with 2 operations.
F, ⎇ AltP
See: Mesh -> Face menu for both.
Note for Blender 2.80 users: Shortcut for Poke Faces was removed and the menu entry relocated to Face -> Poke Faces.
E, Escape, ⎇ AltM, A