You can check that a game is age appropriate by checking its rating. Video games are given age ratings depending on content by the Entertainment Software Rating Board (ESRB). Ratings are as follows:

• C - Early Childhood: Age 3+
• E – Everyone: Age 6+
• E10+ - Everyone: Age 10+
• T – Teen: Age 13+
• M - Mature 17+: Age 17+
• A - Adults 18+: Age 18+

Games are rated for age based the type of content it contains such as violence, language, blood, sexual, drug use and gambling. Most video game stores will verify age before selling a video game to a child, but parental supervision in purchasing is recommended. Here are some useful links for additional information. ESRB Ratings Guide; ESRB FAQ; ESRB Homepage.

Also see,

What safety practices does Microsoft recommend for kids and online games?

What do I need to know about Nintendo Wii security and parental controls?

What family settings are available for Xbox LIVE?