What documents should you carry with you when travelling internationally?

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.

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

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.

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.