I've had good luck with battle starts before - most notably in a sci-fi game which started during the very end of a battle, where it was clear that the PCs faction had lost and it was a matter of getting out before getting killed. That also instantly brought the group together. They were the survivors of Melted Field, hunted by the new government that had taken over, looking to get off planet as soon as possible.

Other fun starts have included a wharf fire (the PCs were agents of the alchemists guild, which meant they had a stall with several barrels of alchemists fire next to the laze), a steam/cyberpunk game where the players all owed medical debt to the same megacorporation and were tasked with paying it off through deeds, the PCs as survivors of a nasty plague that basically eradicated their culture, and the good old fashioned thing in the distance - which in the most successful case was a space ship that crash landed near the PC's wizard tower and surrounding region.