A very simple and obvious example is the administration of taxation, where the government have most of the information already, and the rest is just going through the motions.
The oddest I've seen is the US/Canada air border also improved immeasurably when they laid off loads of Canadian border staff, forcing them to come up with more efficient systems for handling the same number of people with a smaller staff. It's not what you'd call good now, but it's way better.
Ultimately I'd have less objection to the governments keeping data if I saw the benefits from them doing it. As it stands it seems it's just used for their own purposes.