C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
(Click here for a personal note from Marshall Cline.)
Section 27:
[27.9] What header-file-name convention is best? foo.H? foo.hh? foo.hpp?

If you already have a convention, use it. If not, and if you don't need your editor to distinguish between C and C++ files, simply use .h. Otherwise use whatever the editor wants, such as .H, .hh, or .hpp.

We've tended to use either .h or .hpp for our C++ header files.