I'm looking for an app similar to the Nike+ app but for cycling. I'm mostly concerned with distance, calories and average speed. Elevation tracking would be awesome. Does your recommendation pair with a desktop app as well?
There are many apps available for iOS and Android. Some of the big names:
They all have a mobile application that tracks your ride and then uploads it to a central server, accessible via a website. The website often provides reports and breakdowns of your performance.
They also add elevation data, but I'm not sure how accurate it is.
Additional performance metrics can be added through the use of ANT+ compatible devices to allow monitoring speed, cadence, heart rate and many more metrics.
My personal favorite, having evaluated all of them, is Strava. It is free, has a unique feature of tracking "Segments" of your ride, where you can see your performance for shorter stretches of your overall ride, relative to your past performance and also to other riders.
Cycle Meter is by far my favorite due to its ease of use, functionality (syncs with everything), and support. the company rocks, the app rocks, and it's cheap when compared to an standalone garmin.