When you are a convicted felon you notice that many of your rights and freedoms are restricted - your ability to own a firearm, for instance, or your right to vote. What about obtaining a passsport? Actually, felons can usually get US-issued passports - getting visas, however, can be another issue.
What is a passport?
First of all, it is important to understand what a passport is (and also what is it not). A lot of people think that having a passport issued in the US gives you license to travel anywhere you want in the world - this is not the case. A passport is more like an international ID card that has been agreed upon and standardized by different nations.
Since a passport really is just like an ID card, you will not see too many restrictions on issuance of a passport. There are a few exceptions (see below), but for the most part if you want a passport you aren't going to have a problem getting one.
What else do you need?
Typically when you travel internationally you need to get a Visa. Sometimes you can get these at the border (on arrival) and sometimes you need to get them ahead of time. Keep in mind that when issuing a Visa the destination country can do a full background check and decide whether they want to allow you within their borders or not.
In other words, issuing a passport is the US's way of letting you leave the country, but it is entirely up to the destination country if they want to allow you in or not. You probably want to do some research on your target destination to find out how strict they are. Also, consider the nature of your crime - if you have been convicted of drug smuggling you probably aren't a great candidate for a trip to Colombia because they are particularly sensitive to these types of crime.
Severity of punishments
Also, keep in mind that the severity of punishments abroad can be much harsher than US sentences. It is not uncommon, for instance, for other countries to institute the death penalty for drug smuggling. If you want to visit another country you will be best to just keep your nose clean.
Situations where you may be denied a passport