The one thing you want to make sure you do is to not corrupt data that might legitimately be in flash, so if you try to write information in a crash situation you need to do so carefully and with the knowledge that the system might be an a very bad state so anything you do needs to be done in a way that doesn't make things worse.
Generally, when I detect a crash state I try to spit information out a serial port. A UART driver that's accessible from a crashed state is usually pretty simple - it just needs to be a simple polling driver that writes characters to the transmit data register when the busy bit is clear - a crash handler generally doesn't need to play nice with multitasking, so polling is fine. And it generally doesn't need to worry about incoming data; or at least not needing to worry about incoming data in a fashion that can't be handled by polling. In fact, a crash handler generally cannot expect that multitasking and interrupt handling will be working since the system is screwed up.
I try to have it write the register file, a portion of the stack and any important OS data structures (the current task control block or something) that might be available and interesting. A watchdog timer usually is responsible for resetting the system in this state, so the crash handler might not have the opportunity to write everything, so dump the most important stuff first (do not have the crash handler kick the watchdog - you don't want to have some bug mistakenly prevent the watchdog from resetting the system).
Of course this is most useful in a development setup, since when the device is released it might not have anything attached to the serial port. If you want to be able to capture these kinds of crash dumps after release, then they need to get written somewhere appropriate (like maybe a reserved section of flash - just make sure it's not part of the normal data/file system area unless you're sure it can't corrupt that data). Of course you'd need to have something examine that area at boot so it can be detected and sent somewhere useful or there's no point, unless you might get units back post-mortem and can hook them up to a debugging setup that can look at the data.