For me, first game that I ever really couldn't drag myself away from to that extent was the PC version of Deus Ex. I was utterly hooked from the minute I played the sucker, started on a Tuesday evening and for the first time ever didn't go back to work for the rest of the week.
I'd recently had conjunctivitus though, so rather than the usual excuse of a flu bug (seems to be the popular choice), I had a sudden reoccurrence of that

So what was your game, and what was your excuse?