Will there be any issues if I buy a Nintendo Wii from the US and use it in India?
Issues like ports or game campatibility, etc.
I'm not sure about Nintendo's arrangements with India, but I bought mine from the US and I live in SEA. Aside from the obvious connectivity issues everything seems to run smoothly. I can play games bought both from here and from the US.
There's only one situation where your games will not be compatible and that's if the games you have are bootlegged. Be careful of these when buying!
The Wii is region locked, so if India is part of a different region than the US (which it probably is), you most likely won't be able to buy games from a local India retailer, assuming that the games they sell are actually packaged for India. If they buy games from the US and then sell them in India though, you shouldn't have a problem.
The PS3, PSP, and DS are not region locked, so if you're really concerned you might consider looking into one of those.
Besides the region locking which other answerers have covered, you will also need to account for India having a higher voltage at the wall outlet and using PAL instead of NTSC. The first problem can be solved with a generic adapter or (I'd assume) a new power cord from Nintendo. The second can be resolved either through ensuring that you have an NTSC television available in India, or by buying an NTSC/PAL converter.