To play games without downloading, you can purchase game software that does not require an Internet connection to play. You can also play older video games that do not have an online component, or switch to tabletop gaming for an Internet-free gaming experience.
Game software can be purchased online or at brick-and-mortar stores. Recently released games might have an online or multiplayer component, but this is usually optional. Research the game details before purchase to make sure that an Internet connection is not required to play. Most console games, especially portable games for the Nintendo DS or PlayStation Portable, are self-contained and are a safe bet for offline gaming. Older games released before online gaming became popular do not have any Internet options, so look for older games at garage sales and online auctions.
Of course, the most foolproof solution is to stay away from technology entirely and play tabletop games. Board games, card games and role-playing games can be easily played without an Internet connection. Old-fashioned games are often more fulfilling because a sense of connection is fostered by playing with other people. Visit your local hobby shop to see what they have to offer, and invite your friends over for a game night.