I was on a DL redeye from LAX/ATL a few years ago, had just finished the in-flight meal ( yeah...they used to serve meals on airplanes ) and was starting to drift off to sleep when I felt the plan start to descend. I looked out the window and could see the lights of a large city but didn't really know where we were at the time.
The pilot came on the PA and said we were diverting to ABQ for a medical emergency. We landed, the paramedics came on board and took some poor dude off in a stretcher. I thought we'd take off right away again but the pilot explained that because we had to land with a heavy load of fuel, mechanics needed to check the plane and make sure nothing was damaged by landing heavier than planned.
We sat on the ground for three hours or so until they could roust a few mechanics out of bed and get them to the airport to check out the plane.