We fly from the West coast so our preferred 'connection' is in Europe. Typically we fly Delta through either Amsterdam (AMS) or Paris (CDG) and, typically, we make sure it is all one reservation. I say typically because this summer I'm testing a new route out via London and will need to change airports (I have 5+hrs) and I have two separate tickets. I know, I'm crazy. Hopefully it will all work...
In my opinion, the sweet spot connection time is 2hrs. I have, one time, had a connection of 1hr 15 via Amsterdam. The times and prices were great but I also knew that this flight usually lands 45mins early. It did, but I don't think I'd chance anything less than 1hr 30 again.