I mostly use AeroWeather for checking TAFs and METARs, doesn't need much introduction as I think it's the most common app amongst pilots.
Haven't seen many people using fuel calculators yet. I've tried a couple and now use Fuel Uplift Calculator since I find it has the easiest interface. If you fill out the tech log (for myself on a 320), just read all results of the screen. This app checks if the uplift is within limits as well (you can set the limit yourself).
For the longer night flights I sometimes use Distant Suns to figure out which planet/constellation I'm looking at.