I once quit a job after 6 weeks. From the day I started (when I saw my boss for about 30 seconds, was not given a computer or any information about how to get started/set up), it was clear things were not going well. The team I was joining had mostly disbanded (a mix of fired, left for greener pastures, or transferred to another region). As a result, there was no institutional knowledge, just as my team was put in charge of handling an immense new project.

I could see that in the best case, I would be there long enough to get up to speed on my position, just in time to leave. That wouldn't do a service to the company, so I gave my notice after 6 weeks.

To my boss' credit, he offered that I could stick around for a while until I found my next gig. Looking back, I guess this served his interests also — it would have been hard for him to recruit for this position if a newly-arrived team member left so quickly, following on the heels of several other departures.