Android/iPhone and Windows/Mac: Many Flash-based games work better with a retro controller than a keyboard and mouse. The free app WanderPlayer turns your iPhone or Android phone into a controller that already works with 100 popular web games right now with more on the way.
The games vary from Classic Mario to Cannonball (via AOL Kids) to Robot Unicorn (via Adult Swim). Many are retro-styled sidescrollers. If you enjoy playing games such as this you'll probably appreciate the added control, and if your kids are old enough to have your hand-me-down phone they'll get a kick out of it as well.
Keep in mind that WanderPlayer is currently in open beta so a glitch may be found here or there. That said, the developers seem to respond quickly to bugs and feedback. You may want to give it a try if you play a lot of these types of games.