The short answer to this question is yes. You can sue someone from another country just as you can be sued in the United States by someone from another country. There are some laws in the US that pertain to libel and slander.
If you were involved in a libel or slander case your best bet would be to sue the individual in the country in which they live. This is because US slander and libel laws tend to be the most favorable towards defendants. If you sued in the US, the defendant would likely win the case or it would be dismissed.
As for other legal situations, you can hire a lawyer in the country where the defendant lives to get a case started. This can be costly, but you can always research qualified attorneys online to find the right person to handle your case. If you cannot find any other means to solving your issue with the other party, you may find that investing money in a lawsuit overseas is worthwhile.
Suing a person in another country can be expensive. You could also try filing the case in the US. The defendant would likely have to pay to defend their case and pay to show up in court should the case reach a trial.
If at all possible, you want to resolve any issues you have with people outside your country by other means first. If you cannot reach a conclusion and there is enough of a potential judgment that you could be awarded, you might want to go ahead and file a suit in the person’s country of residence.
The best thing to do is to speak with an attorney in the area of law that applies to your case. They can help you determine if it is a good idea to pursue a lawsuit out of the country.