No, I don't believe in death penalties as they are simply too "final". If you've wrongly imprisoned someone you can always release them later and perhaps pay them some compensation for being wrongly imprisoned.
However I don't see any reason against modern gladiatoral combat. Each life-sentenced inmate should be given the option of competing in a series of gladiatoral events (no, not the kind in American Gladiators, but real blood sports). This could be sent on tv as entertainment á la "Running Man".
If they win/survive, they can be set free with some restrictions (like being monitored 24/7). If they don't, well... No one forced them to partake, and they were well informed of the risks.
So letting convicted murderers, rapists and child molesters rip eachother to shreds for the entertainment of society would be pretty ideal. Even if that means that a proven guilty felon "get's out" he or she would've redeemed themselves in the eyes of society by killing others of his or her kind (should help with the rehabilitation process).
So gladiatoral style "public executions" would be fine by me. At least it would be more entertaining than the crappy reality shows on tv now...