Take That are popular (get it from their mums I guess) and for 14 year olds you can't go wrong with The Wanted, Tinie Tempah, Lady Gaga, Bruno Mars. Girls tend to like Glee. Under 16s are more likely to like Eminem. Have a look at the charts.
From my experience (I know a few 13-16 YOs) Greenday, MCR, Radiohead, Dubstep (a genre - not a band) the Foo Fighters, Eminem, Crystal Castles, Tinchy Stryder, The Kooks, Vampire Weekend, 2 Door Cinema Club, Arctic Monkeys, Avenged Sevenfold, Bring Me The Horizon, System Of A Down (who I think are brilliant incidentally).
this is very dependant! my son (13) is into all sorts of rubbish.. NDubz, Slipknot, various others I've not even heard of.
my daughter (17) likes Paul Weller, Oasis, Adele.
Slipknot are brilliant ! (not sure about Ndubz tho)
Here's their drummer in action -pls watch all the way through, there is a surprise worth watching ;-)