I like knowing:
* how many items are in the results
* how many pages there are (a derivative of the first, sure, but helpful to know)
* where I was if I accidentally close the tab and re-open it, or follow a link and need to hit the back button, or share my position with a friend (yes, most paginated results aren't stable in the long run, but usually are in the short run)
* easily jump to either end of the list (or, near to the end of the list, e.g. < 1, 2, 3, ... 98, 99, 100 >)
For example, I follow way too many people on twitter (1700!). I know I'm getting tweets throttled so I miss out on people I care about.
I also know that when I first picked up twitter years ago I made some noob mistakes and followed things I, well, shouldn't have (@Tide? I think a friend was working at P&G or something...).
Anyway, "People you follow" on the web UI is an infinite scroll. Even worse, it's buggy so sometimes you can trigger it to not register you're at the bottom and it won't load. AWESOME. I just want to get to the LAST PAGE. BUT I CAN'T.
And since it seems to load about 10-15 at a time, given that it takes about 1/2 a second to scroll down and wait for it to load, that means it'll take at least 60-85 seconds to reach the bottom - IF it doesn't crash (a reload takes me back to the top). Which means I've never been able to do it.
I had to pay one of those "show the folks you follow that haven't tweeted in n-months" just to try and prune the list, which helped me go from 2,000 to my present number.
Yes, this could be solved by sorting and filtering, but in the truest MVP sort of the world, why do all that extra work just for the "infinite scroll" fad? Switch back to pagination and I could accomplish all I needed and have a nice pruned list. And I bet it's less effort and has far fewer bugs than the current implementation.
I hope that in a few years enough data against infinite scroll will have cemented it as a generally accepted bad idea, only working in a few particular cases.
That mindset of design I think is the next step after "responsive" design. Rather than just scaling the visual design of the page, how about truly designing the user interaction to fit multiple scenarios. If it were up to me, I'd call it Symbiotic Design (responsive 2.0)