FlightStats' PC site is great for travelers and aviation buffs. There's a ton of options and information there like historical on-time data by flight and airline, country by country maps showing all the airports in each country, current weather conditions at each airport, airline and airport phone numbers and local maps.
The FlightStats mobile site (www.flightstats.com/go/Mobile), on the other hand, does only one thing which is to tell you when a flight will depart and arrive. To use it you do have to know the airline code and flight number. Enter those two bits of information, optionally change the date which defaults to today and hit submit. Within a few seconds you should have the current status of that flight.
This sort of simplicity is a real virtue for a mobile web site. Having a single purpose simplifies the user interface increasing the likelihood that first time users will be able to get the information they need quickly and with a low frustration level.