When visiting a new country, you should ALWAYS ask yourself this question as soon as your flights are booked - do I need a visa?
A visa is a way of verifying you're in good standing with your government and to track who is entering their country.
I found a wonderful website for checking this.... it's called www.DoYouNeedAVisa.com :) You select the country your passport is from and then it provides a list of countries you do & don't need a visa for.
New Zealand, for example, allows US citizens to visit for 3 months without visa. A longer stay requires visa application before you arrive. To venture out into Sydney on our layover, we'll need an electronic visa ahead of time (which we've already applied for, here).
Every country has their own rules, depending on which country you're coming from. Some are online (like Australia), some require sending in your passports, some just require a few forms. Do your research and make sure all of your bases are covered.
What if I have a layover in a country but won't be leaving the airport?
Check to be sure. If you land in a country, you'll have to go through immigration once you enter that country.... so having a visa might be part of their process. Check with that specific country (and any other country you will pass through). Better to be safe than sorry!
What if I have dual citizenship (and two or more passports?)
If this is the case, you're in luck. Travel with whichever passport allows you to visit visa-free or with less strenuous rules. Use doyouneedavisa.com to search your destination with both citizenships.
What else do I need to travel abroad?
You ALWAYS need 6 months left on your passport to travel abroad, just to be safe. If your passport is expiring in the next 18 months, get it renewed AS SOON AS POSSIBLE. You can get yourself in a pretty hairy immigration situation if you don't have enough time left on your passport. Better to be safe than sorry, and never travel with less than a year left on your passport.
Also, always have your travel documents handy. If you can prove you're only staying for two weeks they're less suspicious than if you don't have an end date. The more information, the better. Print flight & lodging confirmations and carry on with you.