There are many weather apps for the iPhone, but I'm a frequent user of the free WeatherBug app. The free version was recently updated to version 2.0 with a completely new GUI and added features such as automatic updating of weather data at your current location, along with pollen and UV data for the sun. The app has moved its settings inside the app itself, which is a plus compared to the way it was done before using system preferences.
WeatherBug still has detailed and layered weather maps and a collection of local cameras so you can actually see the current weather, not just instrument readings. You can set multiple locations and check the weather at vacation destinations or just see if Mom is freezing in upstate New York. WeatherBug will alert you to severe weather at or near your location.
I found the app to be stable and easy to use. The screens are much improved and prettier, and the app is responsive to scrolling and zooming. WeatherBug is ad-supported, but the ads are kept to a strip on the lower part of the screen.
The developers also offer WeatherBug Elite for US $0.99, which is similar to the free version, but there are no ads.
WeatherBug 2.0 is a 6.4 MB download and requires iOS 4.2 or later. There is also a WeatherBug app for the iPad which is free, but also has an option for an ad-free upgrade. Some screenshots of WeatherBug 2.0 are below.