Restoring the device might be your best bet, and on the other hand that may not help at all. I know that's not very comforting, but it is a truthful answer.
Try a couple of basic things.
Quit all open/running/recent apps and try using the iPad with only a couple of apps in the recents tray at a time. If you have success, launch a couple more, repeat the process until you crash again. Note the app that you last
launched and maybe it is that all causing an issue. Close that app. Launch another app and continue on until yoy crash again.
If Safari is crashing with regularity - clear Safari and see if that helps.
Go to Settings>Safari>Clear History, Cookies and Data. Restart the iPad. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Hey Fire Bird, although your difficulty may be caused by something you can fix, you may also want to consider that there may be some causes that are beyond your ability to control them in a practical way. I encountered similar issues with my iPad 1 which is one reason why I went ahead and upgraded to the 3rd gen.
One reason apps may crash on iPads is that they run out of operational memory. That's not the same thing as the "Storage" you see in Settings / General / Usage: it's a different type of memory that apps use while they're launched and running. (It's a little more complex than that, but that's the general idea.)
As I understand it, your iPad 1 (along with iPad 2) has 512 KB of this RAM storage. Apple doubled this in the 3rd Gen iPad to 1 GB (1024 KB) of RAM, ostensibly to help support the increased demands of its higher-resolution display.
Over time, apps have become more sophisticated as features have been added, and sometimes that increases the memory that they need to run. The recent shift to support the Retina display in the 3rd Gen iPad has significantly increased the memory needed to manipulate images in most apps (one reason there's been a flood of app updates in recent months).
As you may have read elsewhere, these "improvements" for the iPad 3 can easily have an impact on those of us with older models, because the same app with the high-resolution images for the 3rd Gen comes in the update delivered to our iPad 1s. They're not displayed in their full glory, but they still require the same increase in memory regardless.
All of this increases the "pressure" on the limited memory resources of your iPad 1, and that can easily lead to your seeing an increase in the frequency of app crashes – even if nothing else appears to have changed. Even worse, if a particular app is "close to the edge" in terms of running out of operational memory/RAM, a faster processor can sometimes keep it from dying. (In computers, there's often a trade-off between how fast the processor/CPU is and how much memory/RAM a program needs.)
Not only is the processor in your iPad 1 half the nominal speed of the iPad 2 (which is about the same effective speed as the 3rd Gen iPad), but the 3rd Gen iPad has extra processing resources to stay ahead of the increased demand imposed by its higher-resolution display. Both the iPad 1 and iPad 2, then, lose a little ground because, all else being equal, they're moving a lot more data around inside them (for those high-res images.)
Believe it or not, all this is somewhat of a simplification, because Apple has engineered some pretty amazing mechanisms into their software to minimize the impact of all this extra image data. There's a limit to how effective those techniques can be, however, so you're bound to notice the differences in your iPad's behavior at some point.
As I mentioned in the beginning, this is what pushed me to upgrade from the iPad 1 to the 3rd Gen. I saw the same thing happening that you did and understood that it was most likely something that nobody could fix in the long run. It's an unfortunate fact of life here on the bleeding edge of technology.
So, try some of the things others are suggesting (or may suggest), but keep in mind that there may be only one way to solve your problem, unfortunately.
I did mean 512MB, not 512KB, thanks for catching that. The iPad 2 has twice the CPU speed of the iPad 1 (with more concurrency, meaning processor cores). My conjecture is that advantage may reduces apps' dependency somewhat on operating RAM. But that's just an educated guess. There are so many ways for an app to crash itself, after all!
Good luck, and enjoy your new iPad! Ha, Ha.
Ipad 1 has 256KB of RAM, Ipad 2 has 512KB. So, Ipad1 apps are likely to crash even sooner because of memory shortage ... I have disabled almost all IOS 5 added features, now it runs reasonably well. But, still crashes can occur, Safari runs quite stable though, but some web sites can still make it crash. Also the App store itself crashes regurarly, which I would really focus on solving if I was Apple But since Ipad 1 seems to be forgotten since IOS 6, I don't expect any fixes for this.
The low memory explanation expoused here and everywhere else misses a critical point; the iPad should still never crash! I'm sure Steve Jobs himself would be the first to agree that no device, if properly coded, should ever crash. If the OS that dishes the memory out to the apps was written properly, it would at the very least warn the user of an impending memory issue and offer a gracious escape route.
The common solution offered to "avoid" the bug, which btw didn't exist on my gen 1 iPad until recent OS updates, are only placebos. I have reset my iPad to factory condition and shut off every conceivable feature that consumes memory to absolutely no effect.
Apple take note, stop letting the user community try to bandaid this issue through forums and just fix the **** problem.