I'm a plane-spotter/photographer, and have lived in Phoenix and Chicago. Over the years, I've had a few people at various airports approach me to ask what I was up to. Most of the experiences were positive, with one or two negatives. Here are a few examples:
Post 9-11:
While waiting at PHL to board a flight to PHX, I was taking some photos and writing down tail-numbers. The man sitting next to me appeared very interested in my chosen hobby, and asked me where he could get a copy of the airline fleet-list book I was using. He told me he spent a lot of time traveling, and was looking for something to do between flights.
One afternoon, a police officer approached me on the top of the Terminal 3 parking garage at PHX, and asked me what I was doing. We wound up chatting for about an hour about aviation. He even suggested some other places around the airport for photography!
While photographing planes at GEU one morning, I started talking with one pilot about his plane (a SF260W Warrior), and he asked me if I'd be interested in going for a short hop in it!
Last year, I was spotting/taking photos inside the terminal at MDW. A TSA guy came up to me and asked me (very politely) what I was doing. I told him that I was taking photos and noting the tail-numbers of aircraft. His reply... "No problem. That's OK. Thanks for your time."
At the open-house and airshow at Holloman AFB several years ago, two Air Force cops questioned me about why I was roaming around the ramp photographing the planes and writing down "stuff". (I guess someone had seen me scribbling in my notebook after each shot, and thought I was up to no good.) I showed them the photos and my notebook, and politely pointed out that I wasn't the only person wandering about taking photos. After running my i.d., they got back on their bicycles and rode off.
Pre 9-11:
I was standing by a window at ORD, spotting scope in hand, when a rentacop came up to me and said very curtly "You can't do that here!" My reply to her was "I'm sorry... could you please tell me what it is I'm doing? And then tell me why I can't do it." She just turned and walked away, apparently stumped by my reply.
Incidentally, it took about 6 months after 9-11 for anyone (police, TSA or DHS) to approach me at PHX (where I went almost daily) to ask about my "activities."
Just thought I'd share my experiences with the forum!