For Weather I use the built in app for quickly checking the just the current temp. If I want more in depth I use "Weather Underground".
I also use "Yelp" for finding nearby restaurants with reviews, coffee shops, drugstores, etc.
"Gas Buddy" to help find the cheapest fuel nearby.
"Flashlight" to turn on the rear LED so you can use it as a bright little handy flashlight.
"Allstays Camp & RV" this can show all known campspots (even walmarts that all parking overnight) propane fill-ups, fuel stations, rv dealers, low clearance bridges, etc.
"Dual Level" turns your phone into a quick "bubble" level
"Recreation.gov" you can make reservations through this app and find out info on campsites, same/similar as the recreation.gov website
"SoundHound" or "Shazam" this will listen to a song playing on the radio and tell you the name of the Artist singing, Album, etc. in case your hear something and you forgot who sang it.
"Urbanspoon" , if you are in a city and don't know what you want to eat it has a handy shake the phone feature that will choose a random Restaurant and/or type of food when you shake the phone.
and many, many more