Not often enough for it to be an issue, and I'm writing all the time. If you touch-type, you see when a box pops up. Maybe people should be installing fewer "helpful" applications that end with -gator or -buddy? 
-tranglos
Or AV apps? Or firewall apps? Or low disk-space messages? Or low batteries on your wireless mouse? Or....the list goes on and on and on.
This feature was already present in XP, where you have an option to disable it (i.e. let windows steal focus). Has it been further "improved" in 7? Has it changed?
Yes, MS provided an option to disable focus-stealing in XP. Then application developers started coding around this setting so their apps would still steal focus no matter what the setting had been set to do. Microsoft had enough of wayward software developers not playing by the rules, and rightfully so, and started playing hard ball. I applaud the measure myself.
It's potentially dangerous too, because you may miss notifications that are important (or interesting to you), as they will be obscured by other windows.
No...the taskbar still flashes like a Christmas tree. If you miss notifications by not being able to see that then kindly get thee to an optometrist.
And it's a source of unending grief for users and coders who *want* a focus-stealing popup in some legitimate scenarios (e.g. when you press a hotkey to bring an application to foreground).
That example does not apply here as that is not focus-stealing. Focus-stealing is an app throwing a popup in the user's face without the user's direction to do so. All your hot-keys will still work.
Users who've had problems with this should have taken the issue with application authors, instead of prodding MS to further hobble the OS.
No. The software authors should have followed established programming conventions and rules as set forth by Microsoft. This, IMHO, is a well-deserved newspaper smacked squarely on the guilty authors' noses.
It seems to me that Josh is describing something a little different though - you click to start/open a window/application, and it opens but does not receive focus. That would be unbelievably brain-dead, e.g. start Word, then you still have to click it before you can start typing. Not the same as pop-up dialogs from already running apps. Thankfully I haven't observed it on my wife's installation of 7. Josh, could you please confirm?
When I open an app it will receive focus once it's opened. The only time it doesn't is when I open an app and then I switch focus to an already opened app. Windows is smart enough to see that I want to work with the already opened app right now & will open the new app in the background. Opening an app & not switching focus should open the new app with the focus on it. Any other behavior may be due to a non-Windows 7 compliant program on the computer or maybe buggy video card drivers.