whats the name of the reality show where couples travel around the world, one couple gets eliminated each week?

Your more than likely referring to The Amazing Race. It airs on on CBS

The Amazing Race, is a game show that has teams of two people , who race around the world in competition with other teams. Contestants strive to arrive first at "pit stops" at the end of each leg of the race to win prizes and to avoid coming last, which carries the possibility of elimination or a significant disadvantage in the following race

hope this is what you were looking for

- By the way, you can watch ful episodes @ http://www.cbs.com/primetime/amazing_race/

Travel Reality Shows

We have a show in the UK called COACH TRIP where couples travel around Europe with a similar format - I've applied for the next series

The Amazing Race?

Coach Trip - I watched it for the first time this year and really liked it!

Coach trip?

I hope by "Eliminated" you mean voted off!

that would be the Amazing Race