I really like maps. I have a paper map of the city hanging up on one of my walls at home, and every time I ride a new route, I'll mark that section on the map with a highlighter. Seattle is mostly filled in. I enjoy having scrollable, zoomable topo sat maps that show my latest ride. It's kind of neat, but not as much, to also have charts of stuff that link to the map, so I can click somewhere on the speed graph and see exactly where I was when I hit 43 mph.
Also the (live) speedometer comes in handy fairly often. While I'm riding I occasionally get curious about how much time and mileage I've put in so far, and the feet ascended thing helps me pace myself on long, local exploring rides. Sometimes HR + cad alerts help me stay where I should be, whether it's a training or recovery ride.
It's pretty important to me to have an odometer. Hard to say why. I put the total mileage into a spreadsheet once a week, and have a graph showing my weekly mileage. I like it.
Other than that, I have a folder full of files. Every now and then I'll use them to see how much climbing I've done for the year, or something like that. It's nifty to be able to, but doesn't open many new doors or anything.