The answer is Garry Kasparov.
The women's chess champion for 2008 was Alexandra Kosteniuk.
Chess World Champion
Bobby Fischer is not the current World Chess Champion. Anand is.
Viswanathan Anand is the current World Chess Champion as well as an Indian Grand Chess-master .
Boris Vasilievich Spassky , he was the 10th World Chess Champion .
The brilliant Paul Morphy was both. He was recognized as the world chess champion but before there was a formal champion.
TRUEBobby Fischer became world chess champion in 1972.
The "Lion of madras" Viswanathan Anand of India is the current World Chess Champion .
Alekhine
Viswanathan Anand
Magnus Carlsen is the current World Chess Champion for 2013 . For a list of world Chess Champoins you'll need to refer to the related link below .