Southern White Rhinos are doing well (in terms of numbers, genetically not so much). A few zoos in the US, especially in Florida, are successfully breeding their whites including: Busch Gardens, Lowry Park, Disney, Rum Creek, White Oak, Wilds, and Lion Country Safari. It has been 8 years since the last white rhino calf was born in the US outside of one of these facilities (Audubon, Fort Worth both in 2003). For all the numbers that San Diego has ever had, they have yet to achieve a live birth since 2002.
However, moves will/are occuring to promote further breeding and hopefully start new breeding herds. Of course all of this is mainly due to the number of recents imports of white rhinos from Africa over the last 15 years and the white oak program.
Eastern Black and Indian Rhinos continue a steady effort of breeding. Only recently has the Indian rhino program dramatically increased through an import of 3.0, new private holds, and many new exhibits. The Eastern Black have been held back due to competition with Southern Blacks for space/holding, but will eventually replace Southern Blacks as they are phased out.
Southern Black Rhino program is dead. Many are being sourced to private individuals, mexican zoos (AZA), and non-SSP zoos. I'm assuming that the recent expansion of the planned zoo in Gulf Shores, Alabama for rhinos, will include Southern Blacks.
And the Sumatran Rhino program is now comprised of 1.0 at Los Angeles and 1.1 at Cincinnati.