The Amazing Race is a CBS reality show that started in 2001, and is still on the air. In just recently finished airing season 22, back in December.
It involves 10-12 (usually 12) teams of 2 people (except the family edition season which had teams of 4) who have some kind of preexisting relationship. They race around the world, usually quite literally as most of the routes used circumnavigate the globe. The race is split up into legs. The team that finishes a leg last is usually eliminated, or at the very least eliminated. They usually have to find their own means of transportation, and they're given a limited budget for things like air-fare, taxis, buses etc. Each race typically takes about a month to complete.
Beyond just the racing aspect, there are also tasks that must be completed by one or both team members before they can move on. They're often also given clues as to where to go next, but not necessarily how to get there. OTOH, sometimes they are required to use a particular mode of transportation. There were also Detours, where they had to chose between a harder, but potentially fast route, and an easier slower one.
Contestants could also find/earn special obstacle yards that they could use to screw over another team. A Yield could be used to stop another team of the owner's choice to have to wait a predetermined amount of time before proceeding. And a U-Turn, could force a team to go back to a previous Detour and complete the alternate route as well.
The Amazing Race has won every every Primetime Emmy award since 2003, with the exception of 2010 where it lost to Top Chef. Another interesting factoid: Besides the US, the two most frequently visited countries so far are China and India. There are 13 international versions of the show, including the US.