C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
(Click here for a personal note from Marshall Cline.)
Section 27:
27.1 What are some good C++ coding standards?
27.2 Are coding standards necessary? Are they sufficient?
27.3 Should our organization determine coding standards from our C experience?
27.4 What's the difference between <xxx> and <xxx.h> headers?
27.5 Should I use using namespace std in my code?
27.6 Is the ?: operator evil since it can be used to create unreadable code?
27.7 Should I declare locals in the middle of a function or at the top?
27.8 What source-file-name convention is best? foo.cpp? foo.C? foo.cc?
27.9 What header-file-name convention is best? foo.H? foo.hh? foo.hpp?
27.10 Are there any lint-like guidelines for C++?
27.11 Why do people worry so much about pointer casts and/or reference casts?
27.12 Which is better: identifier names that_look_like_this or identifier names thatLookLikeThis?
27.13 Are there any other sources of coding standards?
27.14 Should I use "unusual" syntax?
27.15 What's a good coding standard for using global variables? New!
[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.