My husband and I gave away our iPad 1s. They were in good physical condition, and the batteries were still going strong, but performance had declined.
Specifically for our uses, browsing became slower and crashes happened with more frequency. So in our case, no, they didn't function as well as they did when they came out of the box. The reason, as shown on diagnostics logs at the time: not enough RAM in iPad 1.
The limited RAM was overtaxed by firmware starting with iOS 5, and with newer apps that had been updated to take advantage of such advances. Other contributors to declining performance: iPad 1s were introduced before Apple launched its version of multitasking on iPads. The hardware was increasingly being asked to do more. Apple realized that was the case, which is why it cut off firmware updates for iPad 1, so that performance wouldn't decline even further.
Any iPad is still better than no iPad, IMO. But if you buy an iPad 1 now, you should be realistic about what you'll get.
I find this response very useful, so thanks. Like an earlier poster in this thead, my wife and I got original iPads when first released and have used them relentlessly since. They are the 16G with cellular models. We've been reluctant to upgrade because they've done everything perfectly and, well, they aren't broken..
But, as it happens, I have been noticing lately that it's been crashing more and was blaming the router. The post above though suggests I might have been a bit unfair on the poor router. On reflection, the crashes don't happen on sites like this, but rather on those of newspapers and magazines etc, where bells and whistles abound. Maybe this is where the RAM limitation is most crucial.
The post above also helps explain another problem that materialised with the upgrade to iOS 5; viz, the time lag in finding a full email address from a prompt. Again, maybe the RAM limitation is one if the culprits; kinda makes sense, I guess.
And worst of all, I've found to my horror that a couple of my fave apps are no longer available for iPad 1 :-(((
Okay, so maybe it's true I have short arms and deep pockets but I suspect now that should a mini with retina display arrive sometime soon, it might be time to make the leap. I reckon I'm finally ready