private const int THE_ANSWER = 42;
or
private const int theAnswer = 42;
Personally I think with modern IDEs we should go with camelCase as ALL_CAPS looks strange. What do you think?
The recommended naming and capitalization convention is to use PascalCasing for constants (Microsoft has a tool named StyleCop that documents all the preferred conventions and can check your source for compliance - though it is a little bit too anally retentive for many people's tastes). e.g.
private const int TheAnswer = 42;
The Pascal capitalization convention is also documented in Microsoft's Framework Design Guidelines.