Here are eight questions to ask. Some may seem obvious, but all too often companies put games on their site without being clear about why they are doing it, or whether they can actually support the game. The purpose of a game can be as vague as to keep visitors amused, or as specific as selling a particular product. In either case a game should serve your business goals. Sometimes the answer to this question will be the same as for the previous question, but people who control web site budgets often have their eyes on different goals.
Most people strongly prefer either word, logic or visual puzzles.
Older people shy away from action games. Web games can be built to automatically collect detailed information about players, but only if these mechanisms are specified up front. To track player-specific information over time you need players to register. Incidentally, the best time to ask a player to register is at the moment they want to submit a high score. This delays the tedious registration process to the last possible moment, lowering the barrier to entry.