For contingent purposes, I always carry the following, in no particular order: Printed copies of my passport and visas (also electronically on my mobile and laptop) Printed and electronic copy of my travel itinerary
(I use TripIt on my mobile, and it's always there anyway).
Printed copy of my accommodation confirmation (if available)
Visa-supporting travelling documents (e.g. invitation letter) Additional means of identification -- be it driving license or national ID card -- in case something happens to your passport.
At the very least, your embassy would like to see these.
I also store encrypted electronic copies of the most important travelling documents on a cloud storage service, e.g. Dropbox.
travel.stackexchange.com/users/793/mindcorrosive
For travel in many South American and African countries you will also need an international Certificate of Vaccination card proving that you have the required vaccinations (eg yellow fever).
While you might be able to get the shots at the border it is much easier (and possibly safer) to get them at home before you travel.
I would also recommend keeping a list of your credit and debit cards together with the phone numbers to call in case you lose them.
In some countries (eg Argentina) you will want to keep proof of purchase of local currency so that you will be allowed to exchange any remaining pesos back to dollars when you leave.
travel.stackexchange.com/users/2971/Michaela Light
Some other documents that haven't been mentioned - some of these may fall into the 'paranoia' category, I'm not recommending all of these for every trip: Loose visas or similar documents not attached to your passport Airline boarding passes etc.
(not just international) Travel Insurance documentation (also, for intra-European travel, the EHIC )
Details of the local consulate/embassy for your home country Copies of past itineraries, boarding passes etc.
for the country/ies you are visting - in case of questions at the border about duration of past visits Company/corporate ID if on a business trip
travel.stackexchange.com/users/2555/Andrew Ferrier
In addition to the other suggestions... Contact details for your banks and insurer in case of theft or lost items or cards.
Contact details for your friends and family.
(Ie.. Got mugged and urgently need to contact your parents?
Hope they didn't take your phone!)
Not so much something to carry but make sure you actually know your email/facebook/etc passwords (and don't just rely on the 'remember me' function when logging in from your netbook or ipad).
[Edit 2014 Feb] Also, you really should be using 2-factor authentication on all important online services (Gmail, Dropbox, Facebook all support 2-factor auth using Google's fantastic Authenticator mobile app).
If you're doing this, make sure you carry some recovery codes in case your phone is stolen.
travel.stackexchange.com/users/2403/Molomby
In addition to all that if you intend to get behind the wheel of a car, plane, boat and so on you will need to carry licenses to that effect such as a driver's possibly with International Driving Permit.
travel.stackexchange.com/users/1372/Karlson
I actually saw this on a list of top new traveller questions, and figured it'd be a good one to have on here.  Obviously with international travel, you'll need your passport, but are there any other important documents you should consider taking with you when travelling?
What documents should you carry with you when travelling internationally?
travel.stackexchange.com
<international-travel><passports><paperwork>
travel.stackexchange.com/questions/9651
travel.stackexchange.com/users/101/Mark Mayo
Printed and electronic copies of: passport, visas, travel itinerary, accommodation confirmation, credit cards and contact details for your banks and insurer in case of theft or lost items or cards, contact details of friends and family. Electronic copies can be stored encrypted on a cloud storage device such as Dropbox. Some countries require an international Certificate of Vaccination card, and in some cases you can exchange money back when leaving if you have a proof of purchase of local currency. If you will be driving, flying etc., take your relevant licences along with international driver's permit if necessary. Many documents may be required while travelling, such as visa-supporting documents, driving licence and bank and credit card details. A vaccination certificate is also required for some countries. Moreover, it is considered a good idea to keep encrypted electronic copies of all these documents.
A number of documents are recommended when travelling, depending on where you are going. These include visa-supporting documents, driving licence, vaccination certificates and credit card and bank details. It also recommended to keep an encrypted electronic copy of these documents.