All of the vehicles in my sig have the original converters, but the BMW is OBDI so I really don't know if those are working or not. I've seen inside them and they are still intact and haven't overheated or anything, so I'm guessing they are.
I had the one on my Jeep replaced last year, it was broken inside and rattling around. It was dented on the bottom so I bottomed it out off-road at some point that probably broke it.