There are error report or log files some where right? Though I am most interested in see if running out of memory is the cause. And on a side, is Team Fortress 2 Large Address Aware?

Assuming Windows - right-click on My Computer, select Manage and go to Event Viewer. Most likely to see stuff in the Application log, I would have thought.

LOL!!! You, sir, win the internet for today xD

Uhm... Debugging the code? :-P

Technically true, although it tends to be useless for games which rarely log to the event log so all you get is what Windows knows about the crash. And that tends to undecipherable code (Stack Error in 000041123x:12312314 or something like that).
Unfortunately, most engines don't do any logging but if it does it is usually located where the executable is and the time stamp will correlate to the time of the crash.

Yes, I tried this to that very result of finding nothing.

TF2 is crashing the most commonly giving an error of could not load lump 53 failed to allocate xxMB. It is very common it seems, many people have this error. It seems those experiencing it all have 4GiBs of RAM. I will have more RAM installed soon maybe that will fix it. But I still would like to know how to tell if a crash is caused by lack of RAM.