When I'm out travelling I prefer to travel light. I keep my iPad and iPhone with me at all times though, using it for reading, as a camera, notetaking and all kinds of other stuff. Below are the apps I prefer the most. If you have any other tips, pease let me know in the comments!
Most of the apps are available for both iPhone and iPad (I'm an Apple guy).
TripIt
Wonderful app and service that automatically scans your mails for travel information and creates itineraries with useful information, such as weather at your destination and changes in your flight schedule. The pro version also keeps track of flyer points.
Evernote
I throw everything in here that I might need for my travel. Scanned documents, such as passport and insurance, as well as flight tickets and random notes. I even manage my budget in Evernote.
Kindle, iBooks, Qiozk
Reading apps obviously. The Lonely Planet travel guides are pretty cheap in the Kindle store, and I tend to buy one for each country I visit because of that. iBooks is for other epub books and pdf's in my collection and Qiozk is for Swedish papers of all kinds.
iCurrencyPad
Great for quick conversion of currencies, useful when arriving in a new country and haven't learned the new currency's value.
Gowalla
I use Gowalla part as a game to collect virtual stamps and items etc (useless, I know, but very addictive), as well as telling my friends where I am.
Yr.no
A pretty good global weather app. Only downside is that it shows a misleading heavy rain cloud as soon as there's expected to be as little as 0,1 mm of rain.
Camera+
I prefer this before the native camera thanks to the photo edit possibilities and the focus option.
Skype
Call home or chat for free, even video calls. Of course I need this.
Google Earth
Inspiration. I can get stuck in is one for hours.
Lonely Planet
Lonely Planet has released a few apps themselves, covering certain cities. Could be useful if you're staying in one place for several days.
Flightboard
Haven't used it that much honestly, but it keeps tracks of flights for a given airport, and it looks good.
TripLingo, Norstedts, Lonely Planet Spanish
My Spanish certainly isn't what it should be and these apps help me to translate certain words or phrases and even teach me some grammar.
SitOrSquat
Find the nearest restroom. Could be priceless (you need to be online though).
TripAdvisor
Awesome way to find the next place to stay or eat! Lots of reviews and tips from other travellers. In many ways I prefer to find places this way instead of from the guidebooks.
Heritage, Qwiki
See photos and information about places around the world. Good for inspiration. Qwiki collects data about destinations from a number of resources online and presents them in a beautiful way.
Sleep Cycle
Sometimes you need to get up early to catch that flight and you don't want to wake up too abruptly, right?
Flashlight
Too see in the dark (duh).
Länsförsäkringar
My personal bank's app. Helps me to keep track of the finances and transferring money between my accounts.