Perhaps this is related. My iPad 2 kept crashing whenever I would double click the home button. I even tried resetting the iPad, and that briefly fixed it. Turning off iCloud syncing and iTunes Match did not work. I finally went into Location Services and turned off everything that did not absolutely require access to the GPS service (mine's a 3G obviously). This has fixed the crash problem for me, so if you have a 3G device I would suggest turning off Location Services for non-essential apps first.
Personally i think you should take it into an itunes store or go in and ask them if they have a solution. The Apple tech team can usually fix it and for cheap or for even nothing ( if you have a warinty on it ). The only problem is they might not want to fix it if it is jailbroken. So if it is jailbroken, the only idea i have is to restore it in itunes and take it in. Hopefully they wont ask.
I have used all of the suggestions everyone has stated so thank you for helping me on that, but I have observed some interesting things that will help you recover your apps:
1) Rebooting your device may only temporarily recover some of the apps but it will fail again, with time being the only matter.
2) Deleting and redownloading an app works but if you have a lot of apps like me then that is too long and time consuming.
3) Turning the power off of the device doesn't help at all.
-Update an app from the app store. Any app. And it just has to be 1 app. This worked for me straight away, and worked like a dream. I'll keep you posted on of this is a long term solution or not!
SOLUTION FOUND: APPLICATIONS CRASH ON IOS 5
I encountered the same problem.
Most of the 3rd party applications would start crashing one day and nothing would help.
If you reinstall any application , all the applications would start working again.
But after some days, the issue would occur again,
It got resolved permanantly after i followed the following steps.
It's been more than 3 months since the application last crashed.
1. Connect your phone to PC
2. Under iTunes, go to iPhone-> Apps
3. Log in to the iTunes store using the same apple ID which is used on iPhone
4. Go through the list of applications. This list would only contain apps that you have downloaded using the current Apple ID
5. The applications that have started crashing would not be a part of this list as you have proably downloaded them using some other Apple ID
6. Delete all the applications from iPhone which are not part of this list
7. Re download the applications using the current apple ID on PC
8. Complete the Sync ( Do not transfer purchases from iPhone)
9. You would not encounter any issues with the applications after this