My iPhone 3GS slowed to a crawl for internet operations like web browsing or using apps, but like magic, it's now ... well ... bearable again. So simple.
Maybe I'm slow on the uptake, but I didn't realise that you have to close down an app. when you've done with it - not just click the Home button.
Try this: click the Home button twice (the round sunken button at the bottom). You'll see all the open apps. in the bar at the bottom of the screen. Scroll right to see the whole line-up. Yes, probably every app. you've ever used. No wonder the thing has slowed to a crawl, it only has a tiny little brain in there.
To close an app.(s), hold your fingertip on one for a bit and you get the red minus signs on them: click to close.
Or, without the red minus signs, just click on an app. to go to it and resume where you left off.