I've just gotta say it, the official Olympics logo usually looks a bit lame on clothing. Further, the Olympic gear is highly time sensitive. Sort of like that Super Bowl XL (2006) t-shirt, it won't be cool for another 15 years, when it finally becomes vintage. The Olympics 2008 merchandise looks neat now, while the games are actually going, but once the craze dies down - the stuff instantly looks dated.
Back in 2002, during the Salt Lake City Olympics, everyone was wearing those god-awful roots stocking caps that looked like they belonged in a Charles Dickens novel. People were running around looking like little matchstick girls. Just terrible.
A number of team sports such baseball (which will soon be discontinued from the Olympics), basketball, soccer, and hockey feature events for both the Olympics as well as a number of world tournaments. In my opinion - unless you are a huge fan of a particular Olympics only sport - consider picking up something for one of these teams rather than that "USA Field Hockey" shirt that might look cool every four years.
A USA baseball hat, Canada hockey jersey, or washed Brazil soccer t-shirt, not only looks cooler, it will be useful for more occasions than a "Beijing 2008" hoodie.
Now don't get me wrong, I'm all about cheering on your country, but I would avoid wearing more than one piece of flare unless you are traveling to see your country play a match. A cool Team USA baseball hat, however, can be worn with a solid t-shirt or polo should to make you look great at any ballpark.
If you are traveling to an Olympic event, consider picking up a simple t-shirt that will look good when handed down to your kids. I would kill for a vintage 1980 Lake Placid Winter Olympics t-shirt.
Final call: If you are traveling to the Olympics, pick up a fun piece of clothing with the year and location proudly front and center. The gear will look cool around your friends when you get home and once it has runs its course and looks a bit out of date, you can save it and pass it along to your kids along with your stories from your trip to the games.
Read a bit more about the tragedy that is Olympic fashion here.