Most of the crashes were reported by players running X-Fi Titanium Fatal1ty PCI-E Sound Cards. If you are using this and enabled Creative Alchemy to work with Max Payne this will cause the game to crash on Windows Vista. Make sure to remove Max Payne from the list of games using the Creative Alchemy lab and the game should run for you.
If this does not fix the problem, you should try to update your graphic card drivers to the latest version, make sure that your system meets the minimum requirements for running the game and that there are no other programs running in the background.
Until now, there were no other reports about Max Payne 3 errors or crashes caused by other reasons, but if you encounter a bug or problem you can’t fix, you can write about it in the comment section below and maybe somebody will have an answer for you.