Toss up: You have to sign up for an account to be able to connect with strangers, but it is easy and painless, and saves your settings and profile so you do not have to enter it each time. - Facebuzz is quick and to the point, a good option for random video chatting as well as text chatting.
While it is geared for adults, they give you the option to skip the ones that perform nude.
Rating: 9/10 Pros: Lightening fast when being connected with a stranger, no wait time. Has alternate sections for those who want clothes on, and those who want clothes off. Arguably the most populated random chat site out there. Cons: There is no real sorting involved, it is hit or miss on who you will end up chatting with. - Chatroulette is another popular random chat site.
It gets a lot of traffic and has had plenty of time to establish itself in the random chat world.
Random webcam chat websites are all the rage these days.