If I want to see what happened eg. get shot on the left leg damage 12
quest completeed XXXXXXXX
etc

If you're on PC you can use the console command "verbose" (there's another one that's does similar, can't recall what it was)
Be warned however that the info will fly by really really really fast if a lot is going on, (edit since it doesn't just log what YOU do, but everything around you) so you'd have to also tell the game to make a log file you can read through later if you're curious.

Not sure about quest logs alone...you could try the "ShowQuestLog" command see if it works.
All console commands list on the http://fallout.wikia.com/wiki/Fallout_3_console_commands_%28all%29 (many, but not all of them, will work in FNV)