The Amazing Race is one of the best reality shows on TV. You should definitely give it a try.
Here's what the race is about. They start with 11 teams of two (except season 8 had 10 teams of 4) and they get a clue to go to a foreign country. The clue will tell them where exactly they need to go, and they find more clues. The clues could lead them to a task they have to do or another city or country. When all clues are found, the last clue will say, "Go to the Pit Stop, the last team who arrives will get eliminated". The Host, Phil K, waits for them all to hop on the mat at the Pit Stop. The last team who arrives is usually eliminated. Sometimes they have non-elimination legs, in which the last team is not eliminated, but stripped of all their money and backpacks, and left with only the clothes on their backs.
And yes, there is fighting! People cut in lines at the airport, and they cut each other off on the highway, and the teammates sometime argue with each other.