Both are correct. It depends whether you want to think of the band as a singular or plural entity. This is a point of difference between British and American English.
In my experience, in American English, people are more likely to do the former (Coldplay is...) In British English we would think of music groups as being plural nouns (after all, there are four people in the band) and thus say 'Coldplay are...' (so the band name would be replacing 'they' and not 'it' here.) It's the same situation with sports teams.

Edit: To confirm what I was already pretty confident of, I just looked at the Wikipedia page of another British band, Radiohead. And the first line reads 'Radiohead ARE an English rock band...' We treat bands as plural nouns in BrE. 

Edit 2: Going back to what I said about sports teams, someone from the UK would write 'Sao Paolo FC are the best team.' 

What a great question Pedro, and for me, being closer to American/Canadian English, Richard´s answer made a lot of sense to me. Yet Paul´s post made me realize a subtle difference that exists between British and American English. So I guess both answers are correct and we can say... Coldplay is/are... Radiohead is/are... Placebo is/are, and so forth.

The Who is/are??? I guess it comes down to thinking about their band name as a group of people or as a single name that represents them all.

Good news Pedro... Your are right.

Coldplay is a Proper Noun, the name of a city, country, person, group of people, etc. and there is only one Coldplay band, so the noun Coldplay is singular. 

"It" is a band and Coldplay is the name of the band.

It is just like saying Sao Paulo FC is the best team.

So, Coldplay is...

Phil's explanation regarding family from the UK perspective is correct.

You now know that there is a common UK variation which you will sometimes see.  However, since the singular form is correct everywhere, you can be safe using it.  This can make your life easier and so I recommend the singular when writing and speaking.