If you're an immigrant to the United States with conditional resident status (which expires after two years unless you take further action) you have, during those two years, the same rights and responsibilities as a U.S. permanent resident. In fact, the popularly used term "green card" is often used in reference to both conditional and permanent residents. Among the rights enjoyed by green card holders is the right to travel outside the U.S. and, more importantly, be allowed back in afterward.
However, there are limitations on the travel rights of conditional as well as permanent residents. By spending too much time outside the United States, or giving up your home base here, you could lose your green card. And with any trip, you can be barred upon return if you've become "inadmissible."
There's an additional concern if you got your conditional residence based on marriage to a U.S. citizen and you'll be spending a long time outside the United States while your U.S. spouse stays behind. Such long separations may make it difficult to prove, as a condition of converting from conditional to permanent resident status, that your marriage is the real thing.
The U.S. government expects that green card holders will really live -- that is, make their primary home in -- the United States. In the government's eyes, someone who just wants to jet back and forth between international destinations, and not really settle here, does not deserve a green card. That conflicts with the desires of some immigrants, many of whom operate on the myth that as long as you return to the United States at least once a year, you can keep your green card.
That isn't true. In fact, technically speaking, you can lose your right to a green card after one day outside the United States, if you left with the intention of establishing a home elsewhere. This is referred to as abandonment of residence. Short trips rarely produce such extreme results, of course -- a person returning to the U.S. after a few days isn't likely to face a lot of questions from the border official, who is the one who would have to raise this issue. But the importance of your intentions, and in some cases being able to prove them, is worth bearing in mind as you make your plans.
In fact, trips of up to six months don't usually raise many questions. However, if the trip lasts longer than six months, the questions you'll face upon return will get more probing. And if the trip is longer than a year, you'll raise a presumption that you've abandoned your residency, and have to work very hard to convince the U.S. immigration authorities otherwise. It's best to be able to show that you were kept away longer than expected, for example by a medical problem or the death of a family member. (Bring documentary proof of such events.)
Any time you, as a green card holder, leave the U.S., you're taking a certain risk. Upon return, you could be found "inadmissible," and refused reentry. The grounds of inadmissibility (found within the U.S. federal immigration law) include things like having certain medical problems (namely tuberculosis), appearing likely to become a public charge (receive government assistance), and having committed certain crimes. (In fact, in order to receive your green card in the first place, your admissibility was evaluated -- that's why you took a medical exam, had to prove financial capacity, and had to provide fingerprints.)
The list of things that make you inadmissible is longer than is found within the grounds of deportability -- that is, things that could land a green card holder in removal proceedings without having left the U.S. first. So if you've become inadmissible, you can often avoid trouble by staying firmly put within the United States until you can apply for citizenship.
If you got your conditional residence based on marriage to a U.S. citizen, then you enjoy an advantage that many other green card holders don't. You can apply for citizenship (to naturalize) three years, rather than five years after getting your green card. (This assumes that you stay married to, and continue living with, the U.S. citizen all that time.) If you got your conditional residence as an investor, you'll still be subject to the five-year wait.
In either case, however, your wait to apply for U.S. citizenship may get even longer if you spend a lot of time outside of the United States. That's because of the requirement for naturalization that, during the three or five years leading up to your application:
If you can't prove all three, you'll need to wait longer to apply, until all three are true.
If you gained conditional residence as a result of marriage to a U.S. citizen, you'll need to prove, at the end of two years, that the marriage is still intact and bona fide. The usual ways to do this involve submitting (along with the required Form I-751) copies of documents showing that you live together, share financial accounts, and so forth. But if you're spending a lot of time in different countries, this task will get harder.
It's not an impossible task, but you'll need to be aware of the immigration authorities' likely concerns, and collect documents proving your ongoing marital relationship. For example, you could show that you made phone calls and visits to each other, set up joint investment and retirement accounts (other than the separate bank accounts for daily, local use), had children together (that's always pretty convincing evidence), and so forth.
If you are a conditional resident who needs to travel for a long period outside the U.S., you risk losing your status if immigration authorities deem that your required residence was abandoned. Before you travel, consult with an immigration attorney about how best to preserve your status, including possibly applying for a reentry permit.