As well as a passport, many countries require a visa to enter. This is simply a document or stamp issued by a country giving you permission to enter for a given period of time and for certain purposes, which is usually stamped or glued inside your passport, or issued as separate pieces of paper.
Here are some examples of entry requirements around the world (check with the country’s embassy or consulate before you leave, though):
New Zealand doesn’t require US or EU citizens to obtain a visa in advance but you do need a return or onward ticket [...]
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Most countries will want to see your passport, but in addition to this there are sometimes other things you need to know which aren’t so obvious. For example, some countries require that your passport is valid for at least six months after you plan to leave that particular country and if it isn’t you won’t be let in. So it pays to get your passport renewed if it is quite close to expiring.
Getting in (and out) of countries can sometimes be a challenge. I once (a long time ago) took a ferry across the Straits of Gibraltar to Morocco (a 2.5 hour journey), only to be turned back as I tried to disembark and had to return to Spain.