There are no more psychos or weirdos on the internet than there are in real life, who you meet everyday. This is because, surprisingly enough, everybody on the internet is also a personal in real life - a person you'd see on the street on an average day. Take the same precautions online as you would in real life, and you should be safe enough.
"Big-name chat sites", to coin the term used above, tend to have a higher incidence of dodgy meetings on them mainly because that's why they became famous. They're known for that, and so people looking for that flock there. This is in the same manner as people seeking hardcore porn end up on redtube or whatever, meaning there's more of that stuff there, but that doesn't imply eff all about the tumblr erotica blog you're looking at.
So avoid sites that are famed for dodgy meetings and instead search for the less-famous but far-more-numerous examples of more pleasant communities, just like Iwaku's chatbox. Most people in real life are generally okay, so the same goes for online; just don't stray into the bad parts of the internet, the same way as you'd avoid a bad part of town.