Should I inherit from std::exception?

The main benefit is that code using your classes doesn't have to know exact type of what you throw at it, but can just catch the std::exception.

Edit: as Martin and others noted, you actually want to derive from one of the sub-classes of std::exception declared in <stdexcept> header.

The problem with std::exception is that there is no constructor (in the standard compliant versions) that accepts a message.

As a result I prefer to derive from std::runtime_error. This is derived from std::exception but its constructors allow you to pass a C-String or a std::string to the constructor that will be returned (as a char const*) when what() is called.