Mass marketers frequently run games and contests on a nationwide scale. People look under bottle caps, collect game pieces, or submit entries in an effort to win prizes. Most small businesses probably don't need (and can't afford) this type of promotion.
However, games and contests can be conducted on a smaller scale. For example, many restaurants ask customers to leave a business card in a bowl. Drawings are held periodically and winners are awarded a free meal or other prize. The restaurant owners, not incidentally, get valuable information in exchange for those prizes. The list of people who submit cards can be used to solicit parties, meetings, etc.
If your business is in an area with a lot of foot traffic, putting a game or contest in the window can draw additional customers into your store. It can be something as simple as the old jelly beans in the jar contest. If possible, use the contest to do double duty: in addition to getting the contestant's name and address, ask for information you need to better market your products or services. Be careful to analyze the results, though. If none of the people drawn in the by the contest become customers, you're wasting time and money. Your promotions must be designed to get people to buy from you; the market research you can conduct is just a secondary benefit.
Whatever games you devise, play fair with your customers. Don't charge them to enter, and be sure to state how and when the winners will be selected, say that the offer is void outside of a certain area and after a certain date, and that any taxes are the responsibility of the winner. And be sure to check out the local laws with your attorney before you start any contest, game, or drawing.