The law requires that you carry ID on your person in all public places. A public place is defined pretty much the same as in the US.
There are three types of acceptable ID. The national ID for citizens, the various type of ID issued to legal residents, or a passport issued by a foreign government. A notarized photo copy of the front page and the page with the entry stamp is acceptable in place of a passport.
The IDs for foreign residents come in many different types, depending on the type of residency. The number formats and length are different for each type. Also, unlike national ID for citizens, this information is not online anywhere. If you need to put an ID number on a form, and they are not going to look at it, just about any thing will do.
US citizens are allowed to stay three months as tourists, which can be renewed, once. Many PTs simply leave the country for 72 hours every three months. There are also people who will take passports and stamp them to show that you have been out of the country for three days. There are many who just overstay, when they leave the county they pay a small fine.
Overstaying can be a problem, because every once in a while, they will decide to ban someone from returning. This happens very rarely, and there is usually some other reason as well, but it is a possibility.
A potential problem with the PT approach is driving. A non-Costa Rican drivers license is only good if the person's tourist visa is valid. If you show a traffic cop your US license, they will want to see a passport.
You can get a drivers license without being a resident. This is the best approach. If you have a CR license and the traffic police stop you, they will not ask to see any other documentation. A driver's license in CR is exactly that. It has a name, picture, issue date and expiry date. That is all. It is not an identity document. It says nothing about your status in the country.
If you bring a car you have six months to nationalize it (pay taxes). After that it must be removed from the country for at least three months. The folks who offer passport stamping services also deal with this. But you could face a problem. A Canadian couple I know did exactly that for a few years. After a while the traffic cops took to routinely stopping them. They figured that they paid less in bribes than they would have if they nationalized the car, so for them it was worth it. For me, I'd rather avoid police attention.
My view is that it is best to buy a car here and avoid all the hassles. Vehicles are more expensive here due to taxes. However, there are good deals to be had. This is a topic for another post.
ID in Costa Rica
Monika says:
The whole situation in Costa Rica is very similar to Poland.
You can go back and forth every three months to keep your tourist visa. In most cases you just don't exist in Polish databases as a resident or anything at all, especially since the aren't as many computers as in the US. The beaurocratic system is so old and extended, potential employers often like to hire people on a "cash" basis- no real employment involved. You don't pay taxes in such situations but there is the once-in-a-blue-moon possibility of getting busted. I've never heard of any ex-pats in Poland who had been "gotten". The Polish-American treaty says that if you're employed in Poland you don't pay taxes in America and vice-versa. If you work on a payed-under-the-table basis you don't get to pay taxes either in Poland or in the US.
Passports are also the id an ex-pat would use even if he/she had a permanent or 5-year residency. Every application for a visa is completely soaked in beaurocracy but in Poland American citizens are treated a bit better than say, Romanians, Gipsies or citizens from the East, Russia, Ukraine, Belarus, so there are rare situations where the visa-worker would give you not-sufficient information as to which and how many documents to supply them with, etc.
The American drivers license is valid in Poland just like the local one.