Tigers in the wild live in Asia, which is where their natural habitats are, usually in areas with swamp and grasslands, and rainforests. There are many subspecies of tiger alive today, and each one living in a different place.
Siberian tigers live in Russia, mostly in the east. Indochinese tigers and Malayan tigers live in areas of South-east Asia. Bengal tigers live in India, and the South China, and finally, Sumatran tigers live, unsurprisingly, in Sumatra!
A common misconception is that tigers can be found in Africa, but this is incorrect.
Lions, leopards and tigers are all members of the Felidae family of cats. Although they originated in Africa, at some point in time, probably around 2 million years ago, a branch of the Felidae moved east toward Asia, and those cats evolved into the tigers we know today. Once settled in Asia these tigers never returned to Africa, although scientists are not sure why.
Of course tigers can be found in other areas of the world, but only in zoos and wildlife reserves.