I've had iOS 7 on my device since it was released to developers last June and I really have got to liking the background fetching feature added to it. I have several apps that make use of it and in some cases, allows me to not even use the app.
For instance, I have OneDrive on my devices for the sole purpose of wirelessly uploading all of my photos and videos to OneDrive (I'll save why OneDrive & not Flickr for another post) and syncing to my computer. This lets me move them in to aperture when I am ready. Never have to plug my phone in, nor open OneDrive on my phone. It just does it in the background for me.
My podcast app is always up to date with the latest and greatest podcasts which is nice and in most cases my RSS reader is updated before I open it.
This is probably my favorite feature of iOS 7.