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For just a quick look at temperature, I use the one by Apple. For more details, I use the Weather Channel app.
 
If you like your apps to look nice and be functional, go with Outside. It isn't free, so I'm sure most people won't go for it because of that, but I love it. It lets you see the weather for the week or for the day with a quick glance, but you can also reveal extra detail. If you need the maps and really high detail stuff then this isn't the app for you though.
 
I've found Weather Bug to be the most accurate weather app for my locations. As others have posted, I use the built in weather app for a quick glance, even though I find it less than accurate in the finer details - for the locations I care about at least.
 
I am using Pocket Weather. I love how it supports push temperature information displayed on a icon badge. I haven't seen too many apps that support that kind of feature. I think they all should since the iPhone OS lacks widgets. I never understood why Apple couldn't support an active weather icon. There's a JB app that does it and worked really well.
 
I use Accuweather and TWC. I find that TWC overestimates chance of rain, whereas Accuweather doesn't (can't say that Accuweather underestimates weather though).
 
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