Very very hypothetical, okay? I have no intention of doing this.
Say you gave out your username and password, or someone stole them, and then that person logged on as you. You’re unaware of them being online, so you sit down to your computer and try to log in.
Would the system register you as already logged in? Would two people be able to post under the same name at the same time?
Ancillary question: When are you logged off? I often log on at work, leave the computer on, and then log on again at home a half hour later. No problems. Does the system log me out after a certain time?
You can be simultaneously logged on at more than one computer. The board doesn’t care (I just did it myself as a test).
silenus, IIRC the board will log you off automatically after 15 minutes with no activity. But even after that time, if you still have the SDMB up on your browser and click on a link (or refresh your screen), you will automatically be logged back in.
My machine at work stays logged in even after a reboot, or over night, so I don’t know about the 15 minutes of inactivity deal.
Not quite the same thing. When you logged in, if you checked the “Remember me” box then your browser will hang on to the SDMB cookie and automatically log you in every time you visit the board.
The way you can tell that you have been logged out is to look at the Welcome message in the upper right corner of every page. It will say "You last visited: [Date] at [time].
Well, as a thought, don’t ever give your username and password to anyone and that won’t be a problem. 
As for theft, I suppose you could tell when some of the forums would show you all of a sudden posting threads about some sort of unclaimed money in Nigeria, and to contact you right away to claim it…
I’ve checked the “Remember me” box and am never logged off. But I’m on a laptop that goes everywhere with me, so sheep-love is probably not a fear for me realistically.
Unless I see a really hot one.
The love that dare not speak its name (and asks for mint jelly) aside, of course you want to be careful with that sort of information, as we tend to roll our eyes when someone presents us with the “my password was stolen and that wasn’t me” story.
We’ll help you change afterwards, of course, but you’ll probably get a lecture at the very least.
TubaDiva
Yes you are. Like nearly every site on the 'Net which requires a login, inactivity of some specific duration automatically kills your session.