Just the plain ol' "Weather" from Microsoft. I choose this because it has offline access. If you try to access the weather on any other weather app, it will give you some error about not being connected. This is important to me because I keep my data off, especially when I'm nearing my cap. The other thing that got me is the solid live tile support. I couldn't find this working well for other applications, especially if data is on and off; other apps would just stop working or just turn blank because my data would be off instead of just caching the last known weather stats. The problem I have is the lack of details and a live tile that adjusts by GPS. In regards to details, hourly forecasts is more like trihourly (which I've come to the conclusion is just enough), you can't click anywhere to find more details as well, like to open a webpage to a more detailed page for finer things. This trend follows into alerts as well. I've noticed a majority of weather apps don't provide alerts, and only a few do it alright to well. This app just provides the title of the alert and the duration. It seems to be enough, but would be nice to see the entire alert, and see what other counties it may apply to as well. Next was the live tile GPS thing. There are few that have a live tile that updates your location. One thing to note though, is that the main weather app when launched will find your location and give you the weather for that area, which I can live with, but this means you either pin the main app to the start screen or just navigate to it in the list; you can't access the main app through a pinned location. With that said, details wise, I think it provides enough, you get the standard forecast, % chance of precipitation, tri-hourly forecasts (which I think is actually ok), extended forecasts, and alerts.
Now why I don't use other weather apps? Accuweather was the last one I was using, but the lack of being able to see the last refreshed weather stats when not connected to data made me leave it, and the alerts were buggy (it would crash constantly trying to scroll through it). AmazingWeather, is great except for the once daily updates on the live tile (which makes having a live tile actually very useless to have, and makes it more of a shortcut than a live tile). Weatherbug just never worked for me (live tiles would just stay that Weatherbug logo (tried both verisons, neither worked)).
For paid apps, I tried out WeatherMaster. I think this was the best one, but it would be off by like 10 degrees sometimes for me, and it didn't provide as many details as I wanted. I wasn't sure if it provided weather alerts as well (didn't see any indication when the others did). It has offline access, and a plethora of details about weather, and it looks great, but it's like $2 if I remember.
EDIT: Pointed out that AmazingWeather actually does have offline access. Still, the limitation of a single live tile update still prevents me from using this.
Facebook
Twitter
Instagram