Yes, bungee jumping should be illegal however people know what the risks are and there are few innocent people who are hurt by it. Thus, there is no significant need to ban the practice of bungee jumping even if it is dangerous to the participants. These people would probably find something equally dangerous to do.
No, bungee jumping should not be illegal. For the vast majority of people who choose to engage in bungee jumping, this pastime has been proven safe as well as fun. As with any activity, there is a fair amount of risk involved. However, bungee jumping has proven itself safe enough to be legal.
There are a lot of activities that are incredibly dangerous that we're allowed to do. Skydiving is dangerous, and even something as simple is driving is a huge risk when you think about it. Bungee jumping shouldn't be banned; if people want to go on thrilling adventures, good for them, but it should obviously be regulated to ensure the highest level of safety.
If people want to jump off a bridge with nothing but a cord attached to them then let them do it. People like to do stupid things so who are we to stop them from doing them. If they obviously don't care about their own safety and well being then why should we?