The annual Free RPG Day is June 18th, this Saturday. Based on the highly successful Free Comic Book Day, it's a chance for the gaming industry to show off new products, give away free quickstart rules or accessories, and get more people involved in our hobby.
See if one of your local game stores is participating with giveaways or game demonstrations. Many publishers also have free downloads for the occasion at their sites or RPGNow/DriveThruRPG.
I always have good intentions about volunteering to run a game demo at a local store but schedules seldom work out. Maybe next year!