I'd been unemployed for about 6 months, longer than I'd anticipated when coming back from working/travelling abroad for a year. My job interview at the office of a car manufacturing company went well and they wanted me. However, there was a job opportunity at the horizon that I wanted much, much more, but *that* job interview was supposed to be on the day the other job started and of course I had no idea what the outcome would be. After a few days of pondering I made the decision to call the car company and tell them I'd found something else, then went to the second company's job interview hoping that I wouldn't blow it and end up with nothing.
And no, calling in sick on the first day to go to the interview (and possibly quitting in the second week) was out of the question for me, stupid as it may sound.
I passed the interview/tests at the second company with flying colours and am still with this company now, 10 years later. Incidentally the car manufacturer got into trouble and fired a fair amount of employees two years or so after I was supposed to start working there. As one of the newer recruits I would have most likely been one of that crowd...
Back when I made the decision I was very aware that I may regret it down the road. I'm still incredibly grateful things turned out as they did.