Interesting that every single response so far has both assumed that the word was used as a noun, and a noun describing a person at that.
Indian to me has connotations with the Indian sub-continent or something that originated there. Nothing to do with Native Americans at all. That's the easy bit.
After that, I find myself sympathising with whoever it was who says the way the question was posed is manipulative - sorry Shanks, I don't mean this as a negative, but how often do you get asked what a word means to you, then have the word presented in isolation? When this happens to me I feel as if someone is going to try and trip me up, and I'm prety sure my reactions/responses are no longer 'pure instinct', which I think is what you are trying to explore.
A strong connotation for me is 'let's go for an Indian' - meaning Indian food. Well, my earliest memories are of Bangladesh, where we lived for a year, and I also spent three and a half years in Hounslow, London, for over a year of which time I had a regular date every Wednesday night at our favourite local Indian restaurant. Now sadly closed down and much missed. (Without trying to trivialise, if any of the Sydneysiders know a really good Indian restaurant here, please advise... Or Max, Shanks, others, do you know and have a recipe for Begum Bihar?)
The other point for me about this word is hinted at in my comment about living in Bangladesh. When applied to people, I've heard it used so often to mean someone from India, Pakistan or Bangladesh, or someone who looks like that's where they came from, rather than specifically about people from India. (I see MAx said that too.) In that context, I have never thought of it as particularly derogatory - uninformed, perhaps, but if you want to be derogatory, try 'Paki'.
..I also thought fleetingly (wistfully - daylight saving has just ended down under and 'winter' is on the way) about Indian summers. Which to me is nothing but positive.
