ISS Visibility does exactly what it promises by telling you when and where to look to see the International Space Station. Transits of the ISS across the evening or morning sky are impressive, whether the viewing is of the space station crossing a broad arc across the sky, or a short appearance that ends in the impressive flickering and fade of the ISS as it crosses the Earth's shadowline from daylight to night. At a price of $1.99, ISS Visibility gives you simple-to-use charts based on your location, and shows you where to look along with a nice 2D map showing the location of the ISS over Earth as it passes your viewing site.
Iridium Flares are bright lights in the sky that shine when Iridium Satellites in orbit around Earth reflect sunlight back toward the planet and produce a particularly bright glint of light in the sky for a few seconds. I find iridium flares wonderful to watch because at their best they flare up to -7 or -8 magnitude, many times brighter than Venus or Jupiter at their brightest. Also, being able to predict these special events is quite a lot of fun. I love to show off iridium flares to friends when the conditions permit. The Iridium Flares iPhone App costs a mere $0.99 but will pay back many times over.
Enjoy these two apps to see things in the sky that will certainly impress you.