Tony provided the needed clue. I was having problems with both Linux and OS X versions of Inkscape but Tony's drawing looked fine. He wrote that he was using a developer build so I installed developer snapshots on both operating systems and the problem went away. A bit of searching of the bug database turned up bugs 1712505 and 1208874 which look similar to my problems.
It looks like the bug will be fixed in the next release. Thanks to all who responded. -TAG
I am using Acrobat Reader 8.1.0 on WinXP SP2 and Inkscape 0.46 Devel built on Sept 5, 2007. With this setup, the gradients appear perfectly - both radial and linear fills. (pdf saved as cairo pdf). I have attached the file so you can test if it is your acrobat or your inkscape.
Thanks,
Tony