No, but other people catch me staring at them.
this, exactly.

although i'm not usually aware i'm staring, but this question makes me realize, usually it happens because i: (one or more of the following)
-am trying to read them or figure out a situation in which they are involved
-am imagining how they must be feeling or putting myself in their shoes
(the above are probably the two most common reasons i stare)
-am trying to catch their eye because they won't make eye contact with me for some reason
-feel more comfortable looking at them than at the others, or they just generally put me more at ease than the others (so i keep my focus on them more than on the others in the group)
-like them very much as a person and am thinking about how much i like them
-find something aesthetically pleasing about them (their eyes, their hair, their clothes, or they are just generally attractive)
-find them absolutely adorable (like little kids)
-find an inner light and kindness shining out through their eyes and face (somehow i just want to stare into eyes like that, and find it hard to look away)
-can't stand the way they are being treated and feel sorry for them
-feel empathy towards them and am trying to to comfort them by giving them a loving/caring look so they feel that someone cares and accepts them as they are
-am lost in their eyes and suddenly the rest of the world fades out until i realize it and snap out of it
-am lost in thought about something and just happen to be looking in their direction and don't realize it right away