In the United States, the answer varies from jurisdiction to jurisdiction. A few states allow felons to vote even while in prison; many allow felons who have served their sentences to vote. There is a chart in this essay from the Sentencing Project.

We might look at the issue from two points of view: justice, and broader pragmatic considerations. At least in the case of convicted felons who have served their sentences, it's hard to see the argument for denying them the vote. That's especially true if we're moved by the idea that by spending time in prison, they "paid their debt to society." But some people also point out that it's generally better for people to see themselves as part of the poltical process. If extending the vote to felons who have served their time makes it more likely that they will see themselves as stakeholders who have an interest in an orderly, democratic society, that's one more reason in favor of the practice.