According to the FDA's website, cups are a Class II Medical Device with Performance Standards.

Cups Approved by the US FDA:
    = MeLuna Classic/Sport -- Jul 10, 2014
    = Femmycycle -- Nov 15, 2012
     = Sckoon -- Sep 18, 2012
    = Rhea -- May 24, 2012 (defunct brand?)
    = Bellecup -- Jun 28, 2010
    = Lunette -- Nov 13, 2009
    = Alicia -- Mar 05, 2008 (defunct brand)
    = (UK) Mooncup -- Dec 26, 2006
    = (US) Moon Cup -- Mar 30, 2005
    = Diva -- Jul 16, 2002
    = Instead Softcup -- Jun 06, 1997 and Oct 05, 1993 (two dates)
    = Keeper -- May 06, 1987
    = Tassaway -- Feb 12, 1981 (defunct brand)

To see the list for yourself, search for MENSTRUAL CUP at http://www.accessdata.fda.gov/scripts/cdrh/devicesatfda/index.cfm

FDA Approval means that they are allowed to be sold by US retailers.  Americans can import non-FDA cups for their own personal use but may not sell them on a retail level.

Edited for clarity.