Seek: for identifying (via live camera or still photos) of insects, birds, spiders, reptiles, amphibians, plants, fungi, and anything else you might find in your yard or on a hike. The regular challenges are fun too. Every person I've introduced to this app has gone completely gonzo. Remember how much of a blast PokemonGo! was a few years ago? This is just like that, except with real things all around you.
Skyview: I paid a couple of bucks for the full version, and use this at night for ID'ing stars, planets, and satellites.
Merlin Bird ID: By the Cornell Ornithology folks, you answer a few questions about a bird you saw (size? colors? what was it doing?) and it makes a pretty good guess of what it was. The same lab publishes a beta app for Android that identifies specific bird calls via microphone. My brother showed me this and I nearly jumped from iOS.
Theodolite: Camera/ARG app for measuring angles, bearing, distance. I use this when I'm eyeballing distant thunderheads and matching them up with I can see on the weather radar websites.
BlitzortungLive: Blitzortung is a crowdsourced global lightning detector. Volunteers run the pi-based detector hardware and strikes are immediately triangulated and put on a map. The live app updates pretty quickly, but sometimes there's a few seconds of lag between a bolt you see and its appearance on the map.
Runner-up: Rockd, which tells you all about the geology you're standing on.