RadarScope - (iPhone/iPad and Android)
Radarscope is by far the most feature-packed weather radar viewing app for mobile devices at the moment. I've been using this app since it was released in 2008 and have been impressed with the subsequent updates that have been applied since. This app is so powerful because it allows you to view radar products like base reflectivity, base velocity, VIL, echo tops, and now even dual-pol products like differential reflectivity and correlation coefficient. If you don't know what any of that means and just want a simple radar app to show you where you are in relation to the storms around you, this is still an app for you. It even displays weather warning polygons, which is essential because you're able to easily see which storms are severe near your location or anywhere else in the US. If you're a die-hard weather geek or storm chaser, this app also accepts packaged weather data plans from AllisonHouse for expanded capabilities. There's even a Mac version of this app that many use in place of the famous GRLevelx suite of radar apps for Windows that cannot run on a Mac.
MyWarn - (iPhone, Android coming soon)
MyWarn is a newcomer to my phone since it just came out earlier this month. Efforts to turn your smartphone in to the equivalent of a NOAA Weather Radio have been made with other apps before, but this app does it differently and simply. MyWarn's one and only function is to alert you when severe weather watches and warnings are issued for your current location, much like a real weather radio. The interface is very clean and there are quite a few settings in the app that allow you to customize which alerts you want to receive. Something I really like about this app that I've not seen in others is that it will alert you when the Storm Prediction Center issues a severe weather risk for your area, which gives the user a lengthy heads-up that severe storms may be an issue later in the day. The alerts are shown in graphical form once you open up the app so that you can see where exactly where you are inside the watch or warning area. The app's simplicity is what caught my attention because users generally don't want to fiddle with complicated setup wizards and a daunting number of customizations. MyWarn is available as a one-time purchase right now, but it will become an annual subscription service for users who purchase after May 31st, 2012.
Weather Underground - (Free - iPhone/iPad [WunderMap] and Android)
Weather Underground has an impressive app because it leverages a few key features that other general weather apps don't have. Besides displaying a computer-generated for your location and a weather radar, which just about every other major weather app does, Weather Underground's app displays weather observations from their network of over 24,000 personal weather stations around the world. This means that you can get more precise current observations for your location because chances are one of these neighborhood weather stations are closer to you than the official observations. The app also displays live weather webcams from users who have opted to put those online along with their current weather data. Finally, and most impressively for weather geeks, is the ability to listen to live streaming audio from NOAA weather radio stations across the country on the smartphone edition of the app. These audio streams are crowd-sourced much like the observations and webcams, so your mileage may vary with availability of these streams for your area.
Soundings Mobile - (iPhone/iPad)
Soundings Mobile is an app that I've only found recently and is mainly aimed at die-hard weather enthusiasts, meteorologists, and storm chasers. This app allows for viewing of both observed and forecast atmospheric soundings at any location where the National Weather Service sends up daily weather balloons. This app displays Skew-Ts and hodographs and even shows a box of stats like CAPE, CIN, LCL, etc that you would find at the bottom of most sounding output pages online. The intriguing thing about this app is that the soundings displayed are not images ripped from the SPC or another online source but rather rendered on the device from the raw data. This means that you can zoom in on and manipulate the sounding without distorting the quality of what you're looking at. This app is great on the iPad but performs well on the iPhone too with an interface adapted for the smaller screen size.
WeatherGeek Pro - (iPhone/iPad and Android)
WeatherGeek Pro is for, well, weather geeks! It is a fairly simple forecast model viewing app that displays model output from the GFS, NAM, SREF, WRF, and RUC models directly from the National Centers for Environmental Prediction. As an added "bonus", you can view MOS output for any location within the app. This is a great app if you need to keep up with the latest model runs without the added frustration of navigating NCEP's website on a small screen. This is not an app I'd recommend unless you have some experience with weather models and forecasting.
These are five apps that I use frequently, but this doesn't mean that there aren't other good ones out there. Leave a comment on this post with your favorite weather apps!
(Disclaimer: I did not receive compensation for or was asked to post this list of apps. These apps are merely ones that I use and enjoy personally and I receive no financial incentive for mentioning them on this blog.)