Sometimes whether we're actually still here or not. When I'm on my own computer I don't bother to log out or in. It takes the system an hour or so to log me out if it hasn't heard from me, whether because I'm really not here any more or because I'm writing something really long. I don't notice because I get logged back in automatically.

I'm not on my own computer right now, though, so as soon as I finish whatever I came here for, I do log out. That could very well mean I really am offline two minutes after posting.

When someone's "visible", there's a line on their profile an inch or so below their username, something like:

Last Activity: Today 06:12 PM

If that isn't there, they've opted for invisible mode.