Any Coldplay fan will immediately direct you to Parachutes, their debut album. It is a wonderful piece of work. You should start there. I'm a big fan of the song "Trouble" in particular. From "A Rush of Blood to the Head", try "God Put a Smile Upon Your Face", "Green Eyes", "Daylight", and "The Scientist". That album also has what is arguably their most popular song, "Clocks". On the CD X&Y, standouts include "A Message" and Square One". Finally, Viva La Vida has "Death and all His Friends" which is a pretty solid song, at least in my opinion.

The EP that Life in Technicolor II came off of, Prospekt's March, has another good track that's worth listening to. It's called "Glass of Water." Try that one too.