TinkerCAD is used a lot for 3D Printing, but at the low end.
At the higher end, there is http://onshape.com, an online professionally-oriented CAD tool that is aimed at mechanical engineers. Onshape is from the team that brought you SolidWorks.
While http://Clara.io does have some capabilities for 3D printing, it is best to think of Clara.io as like an online Blender with publishing. Like Blender, Clara.io is oriented towards media creation (stills, animations, videos, etc.) but not necessarily restricted to solid models.