Crucifixion
In light of Easter just ending, this form of execution is pretty high profile, and one of the most barbaric. While most think it’s the nails in the hands and feet and the exposure that’s the worst part, it’s not. It’s what happens afterwards, which is why the Romans loved it.
When a person is nailed to the cross, they’ll instinctively try to support their weight on their injured hands and feet, but eventually their strength gives out. As their legs fail, their arms are pulled from their sockets and the chest hangs down. This makes it impossible to fully exhale and the carbon dioxide levels in the body increase until you suffocate.
This whole process could take hours, if not days, and was a source of entertainment for the Romans. They’d wage on how long people would last, and sometimes, if they were feeling humane, they’d speed along the process.