Pop Rivets

I mounted towel bars by making little backer plates of thin plywood neatly painted, which look a bit like blank wall plates for electrical boxes. I glued them to the front of the wall (mainly to keep the plate in place while mounting stuff--not a super strong permanent glue), and drilled through both the plate and the wall to use standard plastic wall anchors. The backer plate is intended to do two things: it provides sufficient thickness for the wall anchor to work properly, and it helps to spread out the stresses from the mounting feet of the towel bar and prevent puncturing or tearing the wall material. Time will tell how effective this proves to be, but so far everything is fine and looks decent.

If you can attach to the "studs" or similar framework in the wall, that's by far the best solution.