Multiple rights are lost as a direct result of a felony conviction, but I don’t think that includes obtaining a passport. A passport is essentially an identification document. If the crime was related to something that might pose problems with traveling in and out of the USA, I’d be more likely to say no. Treason, terrorism, drug offense (international), etc.
I believe if you owe a certain amount of back due child support you will also be denied a passport.

I’m not 100% certain of the above, so wait for other responses before you go on my word completely.

If you did your time and paid for your crime. You can get a passport.

You can get a passport, but when you have to apply for Visas for countries you need to travel to, you may have a problem. Even Martha Stewart couldn’t go to the UK.

I agree with @cazzie, getting the passport will be the easy part. Getting permission to enter from the country(s) you plan to travel to is going to be the hard part.

It won’t be impossible, but you have to start the application process well before you show up at the port of entry.