These are all for Android...
Radar: None of these have forecasts or current conditions for your area, they're just radar apps.
Raindar is a great radar app but it doesn't have all the radar features that are available in something like Pykl3. It's essentially a mobile version of Weather Underground's wundermap. It's free and I love the look of it but I like the features of Pykl3 more.
Pykl3 has relative velocity, spectrum width etc, and all the dual pol radar products for sites that have dual pol. Pretty much all the Level 3 radar data the NWS releases is available with Pykl3. It can also use third party data from Allisonhouse.com, and if you're on spotternetwork, it will update your location with them. Radarscope is similar but I haven't used it because the reviews on their market page weren't as good as Pykl3's. Unfortunately neither has a lite or trial version.
General weather: your forecast, current conditions, high/low, sunrise/sunset etc
There are a ton of weather apps for this. Weather.com, weatherbug, etc, just pick the one you like. I've found one company named WSI Corporation makes apps for a lot of TV news station weather departments. They all look the same but each one is branded for that TV station and only has data for that area. It's pretty good though, all the forecast, current conditions, a basic radar, and none of the junk that some of the larger apps have. It might be worth searching for "WSI Corporation" and seeing if your local TV station has one of their apps.
Misc:
Simple Weather Alert. Set your area and decide which alerts you're interested in, and it will warn you when your area gets an alert. The notification method is customizable so you can have it vibrate for a wind advisory and turn the volume all the way up and scream like crazy for a tornado.
WeatherGeekPro has a ton of forecast model maps. NAM, GSF, RUC, WRF, SREF, all with multiple hours into the future and all with multiple parameters for different mb heights and various forecasted readings. Example, the GSF model has 11 different parameters and hourly models for 24 hours, so that alone is 264 GSF maps.
Beat the Traffic. Not necessarily weather related but it can be. This app is for viewing department of transportation webcams all over the US, mainly around large cities. I will sometimes watch a nasty storm on radar and open this app to watch it on camera.