I think it's OK if the parents are OK with it. Preferably something cheap that can't go online.
Pretty shocking that someone has given them a phone without your consent/knowledge though.
My cousin has two daughters and I think they got phones around the age of 8-9.
In terms of what age is the right age, where do you draw the line.... I don't know, I reckon by the time kids get to about 14 or so they will probably be really keen on having one, one thing to bear in mind is that you don't want to stunt the social growth of your kids by cutting them out of the loop on such things. I didn't get a mobile until long after I left uni (I was one of the strange people that adopted online communication, mp3 player etc long before a mobile!) but times have changed, they are an integral part of society now and there's always a chance that teenagers could get laughed at for not having one or feel excluded when others are making arrangements etc. @Leviathon, you may have been 19 when your got your first mobile phone but that was ~1997 so still a pretty early adopter, I'd wager you were well below the average age of a mobile phone owner then, maybe even a bigger difference than between the current average and 15-16 (speculation on my part but I knew very few teenagers with mobiles back then, nowadays the majority seem to have them).
As for checking a phone I think where 11 year olds are concerned you are within your rights to check it if you are the one paying the bills.