I'm from India and all my life I've pronounced 'often' with 't' silent. Since we follow British English, I assume British people say it the same way? I guess in American English, one pronounces it with 't'. What are the rules about this word in other varieties of English?
Pronunciation of ‘often’ does not inherently depend on dialect. See: How should "often" be pronounced? (possible duplicate).
I'd say that it's a dialect thing. I often hear people pronounce the 't' in 'often'. It annoys me, because I grew up with it silent, but it's not actually wrong in any sense.
I'm British, by the way. I hadn't noticed it (the pronounce 't', that is) being an American use at all (but now I probably won't be able to stop noticing it). It seems to be increasing in Britain, though.