iPhone Apps

Gaia GPS for offline Topo Maps (used to supplement the paper maps and compass you should be carrying).

Camera+ for taking better pictures with the iPhone.

Just switched from iphone to Android-based Galaxy II S. I am very happy with the switch. Gaia is on Android too.

No Android for AT&T. I could jailbreak one but it'd cost me the price of the phone, and all the apps. I'm upgrading to a new iphone4s for free!

Camera+ for a better camera.

MyRadar for a location-based weather radar.

Yelp! to find a good restaurant after your hike.

Wilderness first aid. Columbia Knot app. Backpacking gear list. Kindle or other book app. Podcasts!

If you want to use Gaia or other gps functions, you'll need a battery charger. I used suntactics solar charger on
My JMT trip this past summer. It is kind of pricey, but it worked great. I highly recommend especially if you like backpacking and like your iPhone.

Gram Weenie for listing all of your gear with weights and then creating trips lists.

Here are my favorires:

WinkPass Knot Guide
+1 on Gaia GPS – very easy to download waypoints
Peaks
Clinometer
Planets
Star Walk
Meteor Shower
National Parks Maps
Calparks
Yosemite (Chimani)

So much FUN!

Ones I use not already listed:
Mammut packing list (free)
WikiHow survival (you never know)

Looking at:
Commander Compass
Backpacking Checklist
Survival Pocket Ref

I also ordered, but have yet to receive, a mophie outdoor battery with Accuterra topo software, Amazon had it mis-priced at $30 when it should be (and now is) $119:
amazon link

I am maintaining an annotated list of iPhone gps/mapping apps which you ought to look at to learn more about the options. There are 6 or 7 worthy choices (including Gaia GPS which has already been mentioned). There is no one app that does everything, and if you’re serious about mapping apps then you’ll want more than one. For use in the U.S. I regularly use four: Topo Maps, Gaia GPS, GPS Kit, and Maplets

And, to learn more about how to deal with battery drain and how to choose a gps/mapping app, you ought to read the Instructions for using iPhone as Backpacking GPS/Mapping device.

Since getting my iPhone, I have used it on a six week hike in Australia, a six week hike in Turkey, and many shorter multi-day hikes in the Bay Area. Other than mapping/gps, the iPhone apps that I use while backpacking:

Michael Morcombe eGuide to the Birds of Australia, Birds of Northern Europe. Sibley eGuide to Birds of North America.
Pano (a terrific little app for taking panoramas)
Read It Later (for saving wiki pages to read offline)
GoodReader (a nice viewer for a wide variety of document formats including doc, xls, pdf, etc)
CSV Touch (for lists of things I want to have with me)
DropBox (can’t live without it, for sharing files between iPhone, desktop, laptop, husband’s laptop)
Emerald Chronometer (for sun, moon, planet info; and because it’s hands-down the most beautiful app I own)
Shralp tide (free easy tide charts)
RiverGuide for Kayakers (nice view of the US stream flows, requires connection, so useful for planning a trip, but not while in field)

The Photographer's Ephemeris (TPE). Gives you time and direction of sun/moon rise/set and for current – or any other – location. Also tells you when twilight is. Can compensate for mountains. If you have 3G signal or run it before leaving signal, overlays sun/moon directions on a map or aerial photo.

Not sure what outdoor specific apps means to you — for longer trips, a lot of other stuff gets relevant. Like having good web sites to get weather reports that are most relevant to where you're hiking. A voice recording app is quite handy on my phone. Good keyboard software (or in my case, hardware) for journaling. Whatever software works best for you to upload your photos to whereever you care to upload them.
I'd also think in terms of getting pdf documents about equipment that you own and having that sort of thing on the phone. Definitely a book reader app, music, and perhaps audiobook content. Think also about some sort of podcast software.

I don't have an iPhone so won't suggest specific apps; I think if you know what you're looking for you can see what's well rated on the market and try something out.

When backpacking, the apps I use most frequently are the camera, and things related to journaling, with infrequent internet access coming after that (weather reports, checking email etc when possible).

Oh, an app that activates your flash as a power-draining flashlight can be helpful for changing headlamp batteries in the dark. And at this time of year a good alarm clock app is helpful, though I think the one that came with my phone works fine.