It's true that most adult Indians don't wear shorts. However, I think in most cities and at tourist sites people are quite used to seeing foreigners in shorts. So if you're comfortable in shorts, that's quite all right in most places in India - but not the super-short ones mentioned above. Also note that entry to some religious spots may be disallowed if you're wearing clothing that's considered too revealing, and that might include shorts.

Most casual clothing will be fine for tourists in India as long as it isn't too revealing. As others have mentioned, there will likely be some staring regardless of the clothes.