Joe Satriani, as the guitarist is accusing the band of ripping off his 2004 track “If I Could Fly” for their own Grammy-nominated hit “Viva La Vida.
http://www.rollingstone.com/rockdaily/index.php/2008/12/05/joe-satriani-sues-coldplay-for-viva-la-vida-plagiarism/

The news is all over. While people have different opinion, it is very clear the melody of Viva is exactly same of Joe. Another indie group from NY(The Creaky Boards) has also claimed it was theirs copy, but their is a bit different. In the past, Coldplay has also been accused of copying a tune from a Berlin based band, Kraftwerk, and using it in one of their album. Coldplay has been getting away so far, but this time, they have met their match-one of the greatest guitarist alive on this planet. Joe has his own following and is NOT very well know in the mainstream music industry. Joe is a very respected musician who has taught in Berkelee and has been the "Guru" of many now famous guitarists including Metallica's Kirk Hammet, Steve Vai (another virtuoso guitarist) to name a few.People who listens to pure rock will know him very well. Now colplay has earned a lot from this Viva song and grabbed a Grammy award, it can all go to hell from here. If Joe wins the case, Grammy will be stripped and they'll have to share all the royalties from the past and the future with Joe.
There were very accurate comparison on youtube, it is surprisingly clear they both sound alike in terms of rhythm, tempo and melody. But all those yuotube video has been removed as requested by coldplay's record company. Wink Wink, somebody looks scared when things are exposed.

This music teacher does a better job explaining in terms of music.

Here's a video, still floating around with Spanish subtitle making comparision of the two songs.