You never know when you'll need it and it will help when travelling in areas where coins are not accepted or when you don't have change. This really is one of the most important things you can do whilst travelling on your own. This is your chance to meet cool people from all over the world. If you're someone who wants to go out and party, it's always easier and safer to find yourself a little group to hang out with at a club or pub. People will be more friendly and accomodating to you if you're on your own.
Strangers can be cool.
Obviously, if you get the feeling someone is a freak, keep walking. But sometimes you can find yourself in the coolest conversations with complete strangers, only to discover at the end that you're not really strangers anymore. Go on tours for young people. Go on tours period. It may seem more exciting to do it all yourself, discover things on your own, and just take your time, but you'll miss a lot that way.