How about this for an example. I run NewsRob on my Nexus One. It's an offline RSS reader, which periodically downloads the articles and web content in the background. It does this seamlessly and transparently, without me even noticing. When I fire it up, the content is all there, cached locally on the device - so I can read my feeds regardless of whether I have a signal or not.
The closest equivalent to this on iPhone is Bylines. It can't sync in the background, and (I believe) can't run as a scheduled job in the background). So you have to have the download running in the foreground, which means that while it's downloading the content you can't do anything else. Which, frankly, is a total FAIL.
There are many other examples. I have a twitter app which refreshes my twitter feed periodically in the background and notifies me of mentions or messages. I have FoxyRing which runs in the background and every 10 minutes or so it checks the ambient noise level and sets the ringtone volume accordingly. I have a wifi app (Y5) which tracks my location, and if I'm in the same area as an SSID that I've connected to, it automatically enables Wifi (and when I leave that area, it switches wifi off again to save power). Another service I run in the background is 'Screen On', which monitors for certain applications running foreground, and if they're detected it switches the screen timeout to 'infinite'.
Now, some or all of those features, you could argue, could be part of the OS. They could also - with some hoop-jumping - be managed using notifications from the OS location/device state subsystem. However, that all requires the OS vendor to provide those functions. And the RSS download one simply isn't possible at all without it preventing me from using the device to do other things concurrently to the download.
Lots of people say "but I don't need multi-tasking" in justification of the iPhone's draconian limitations. Personally, my device would simply not fit my needs or requirements if it couldn't have background services running....