Horse Races Now is a handy free app that can turn your iPhone into a complete racing program. After signing up for a free account, you can look at the racetrack info closest to you, or anywhere else in the US. The app features live streaming video, and race replays go back up to two years.
You can set your favorites up (tracks, horses, jockeys) and get push notifications of the latest results. A search engine provides access to info and replays from every North American track.
Notifications include Entry, Call to Post, At the Gate, Results, Replay and Chart and Workout. The app is easy enough to use, and includes a help screen.
The app gets good reviews, and it is complete and easy to use. Some tracks don't send their video feeds, which can be frustrating, but the app developers don't have much power over that. It's up to a particular racetrack.
If you are a horse racing fanatic, then this app will give you a lot of useful information. It requires iOS 5 or greater. It is optimized for the iPhone 5, but is not a universal app.