I understand your discomfort. It would seem a bit odd to me if someone sat right next to me if there were many empty rows of seats available. Personal space is to be respected, especially in some cultures. Other cultures not as much. That's something to consider.

I agree with another poster that if you feel very uncomfortable, there is a suave way to move. Maybe smile at the person and say "Oh, I'll give you more room, if you like" and then swiftly move elsewhere. If they say you don't have to, just say "No, no, I'm going to move", and swiftly do so, firmly saying "Excuse me", if needed. Or maybe say "I'm going to be getting off at the next stop, so I'll let you have more space", then walk towards the subway/train door and sit closer to it after 30 seconds, or even move to a different train car.

If a train/subway if full, you're going to have to accept the person next to you. You can always still get up and stand. That's you're right. Sometimes I've moved in these cases, especially if the person stinks, seems annoying, intimidating, or similar.

Trains I take to NYC, or the campus buses I used to take when I was in college, were often extremely crowded. I actually didn't mind at all. I like being near people, usually, but I don't invade strangers' spaces. I do remember always sitting right up against my sister growing up. She'd usually elbow me and yell at me to move over. Yea, some people like that comfort. I do remember at college spotting this guy I had been enamored with. I sat right across from him deliberately and smiled at him. We exchanged a few words. Nothing came of it, but I was smiling for the rest of the day.