I use Training Peaks and Garmin Connect. They both have pros & cons, so I use them redundantly. Training Peaks tracks mileage on my shoes, and it's what my HIM plan coach uses to look at my progress. I have the free basic version so there is a lot of functionality I don't take advantage of. I use Garmin Connect mostly to keep my collection of route maps. When I want to go run or ride X miles/minutes, my workouts are searchable by distance or time. It helps me get out the door faster than coming up with something new.
I don't think either of those link to MFP. I use MFP, but I enter it all manually when I'm using it. I have a mapmyrun account too, but I really only use it to plan routes, and on my iPhone when I'm on vacation/traveling and didn't bring a Garmin.
Some people also use RunKeeper but I haven't tried it because I already have stupid-many accounts for the same stuff.