When inspecting another player...

Are you completely conspicuous?

Or do you try to position yourself in a not-at-all-suspicious way, click on them and then run off with the character window while praying and hoping they didn't notice you?

i stay at place and look at it

There are two ways I do it:
1) In passing while running another way without stopping
2) Walking up to that person and poking them; If they look back at me, I press /welcome and run off. If they don't I only run off.

Haha, so I'm not the only one! ;)

Both, actually. If it's someone I know, I'm pretty obvious about it. Even with strangers, if I know them to be socially very interactive.

If I don't want the other one to notice I am spying on them I stand as far away from them as possible so they don't notice me, or if it's close to an NPC or a retainer bell I just click on a few other people too in rapid succession, to make it seem as if I was just going through tab targets xD

Clicking on the ground to deselect your target is your friend.

well..

heres me trying to not to look like i have noticed the other catman noticing me...

http://i.imgur.com/ZAVeu35.png

I get as far away as possible so my target doesn't see me, and I start snooping.
And sometimes in reverse cases, I lock eye contact just to make the person who is inspecting me nervous.

My favorite is when people walk a few steps past you when checking you out, but stop and do the little look back over their shoulder like you're not gonna notice. Any time I catch someone looking at me, I always greet them with a bow, pat, or wave..

You'd be surprised how many people run off.

I try to do it on the sneak, if I get caught I /hug them.
If I catch someone looking at me I /throw.

Just put your mouse over the person and type

/c <mo>