Also like to remember childhood Flash games, and recently faced the same problem - many of them simply do not work. But there are a few sites where you can find emulators to run these games. For example, Flashpoint is a great project that has saved thousands of games. So I advise you to look there. And if you want to try something new, there are dynamic arcades, such as slopegame-unblocked where you can relax playing directly in the browser without any fiddling.
