The new version of Chatroulette is quite restrictive and bans users for various, unknown reasons.
There are no official announcements explaining the banning process, but the Chatroulette terms of service state clearly that the access to the service can be restricted anytime without notice:
Chatroulette reserves the right, at its sole discretion, immediately and without notice, to suspend or terminate your access to the Web site, Content, or Services or any part thereof for any reason, including without limitation any breach by you of these Terms. You agree that Chatroulette shall not be liable to you or any third party for any such suspension or termination.
The reason of concern is that Chatroulette seems to snap a picture and store the image of every user along with the corresponding IP address. Based on this info users who are reported (using the "Complain" button) receive a temporary ban.
How long is temporary? Based on users reports it could be minutes or hours, but appears to vary greatly. This is probably due to manual review by moderators that have access to associated logs (images, ip address, location, etc). Users who are violating the service's terms may receive a permanent ban.
Important! This is not official information, simply conclusions and opinions based on the data available.
Bypass Chatroulette Ban
The solution to unban Chattroulette is to change your IP address. This is also recommended in order to protect your privacy while connected.
There are many hide/change ip solutions but, probably the best one, is by connecting to a VPN service. VPNs provide a secure, encrypted tunnel between you and the company renting the VPN, thus hiding your real IP address.
You can choose between free, ad-based, VPN solutions like Hotspot Shield or Expat Shield and paid VPNs, that provide premium service with various locations, unlimited bandwidth and high speed.
After you get access to such a service, all you have to do is to make sure you connect to a VPN server before loading the Chatroulette site.
The conclusion is that it's not difficult to bypass Chatroulette ban, but, for your own safety and privacy you should hide your IP address everytime you access Chatroulette.