This app was mentioned in 7 comments, with an average of 2.29 upvotes
I use NWS Now
https://play.google.com/store/apps/details?id=com.joeperkins.nws&hl=en
Pros. Totally Free, No Ads, and data comes directly from NWS. It is also one of the few apps that let you read the local weather forecaster discussion from the NWS.
Cons: Compared to other apps retrieves data much slower. Compared to other apps some features may be missing (e.g, no up to the minute forecast).
A little late to this, but I recently started using this NWS app and I love it. Just thought I'd bring it to your attention since it's not one of the big boys.
This one is the one I have. It is pretty good for not having fluff.
I haven't tried using it, but the National Weather Service has an app. It says it does weather alerts.
I like this one for Android: https://play.google.com/store/apps/details?id=com.joeperkins.nws
http://www.weather.gov/ and by extension the NWS NOW weather app
In my opinion it's the absolute best weather service there is. The website is streamlined, simple to navigate, and contains all the information you could ever need about weather in your area or abroad.
What's the best part? Absolutely no ads. It's a public service that we pay for with our taxes, so everything having to do with the NWS is completely free of advertising.