You see, cgminer's developer has decided to stop supporting GPUs. I don't blame him -- he's probably earning a ton of money working on developing and maintaining his program for ASICs, and since he's only one man he can't really keep doing both. But it means that code that worked fine in the past may now have difficulties. And that's exactly what's happening.
With their Hawaii architecture, AMD updated some things for the R9 290/290X. Specifically, they've updated their Overdrive engine from version 5 to 6, which helps with things like preventing the GPUs from frying if you run them too hard. This is part of the reason why you need to carefully tune your mining rigs for each GPU -- one R9 290X may run great at 975/1550 clocks while another will totally fail at those speeds. You can often see that you've pushed the GPU engine clocks too far by watching the clocks in MSI Afterburner; if you've set the engine for 950MHz and it's bouncing around between 800-950MHz, AMD's hardware is doing its job and dropping clocks to reduce power draw and protect the chips. Drop the engine clocks 25MHz (or 50, 75, etc. MHZ) and see if clocks go up. But I digress....
So the problem with R9 290/290X (Hawaii) and BSOD/crash on exit is that cgminer is tying into older software/hardware paths that don't behave quite the same on the latest GPUs. When you exit normally and cgminer tries to release things, there's a glitch and a BSOD is the result. Note that this happens on Windows as well as Linux (though without the BSOD on Linux, obviously), so it's not just an OS problem. But what's the solution?
Update: Forget everything below this point! There's a recompiled version of cgminer available that fixes the problem, and I recommend using it.
[Old text follows so you can see how things have developed.]
Simple: don't use any of cgminer's GPU overclocking and/or temperature monitoring features. That means you have to avoid the following (as far as I can tell):
For what it's worth, I'm still using cgminer to control things. I tried playing with MSI Afterburner to get things to work "properly", but getting everything to persist between reboots isn't something I've fully figured out yet. When I do, I'll post instructions.