The SBS Tour de France Tracker is a free app offered for both iOS (iPod Touch/iPhone version and an iPad version) and Android. Unfortunately the key feature, live video streaming of the Tour, is not available here in Canada but that doesn't mean that it isn't a handy app. There is a live news-ticker of the latest movements within the peloton (including break, chase, speeds, etc), a full standings list (including General, team, sprint and King of the Mountains), a full description of every stage (including a historic look, fully interactive Google Map of each stage, elevation profile, latest news and results), and a listing of all the teams and a profile of each member. It's a pretty slick app (especially for free) and easier to navigate than trying to find the same information on a web page... that is why it has been my go-to app for Tour news.
