<p>Is <a href="http://en.wikipedia.org/wiki/OpenID" rel="noreferrer">OpenID</a> a secure method of authentication users on a website?</p>

<p>And, if not, what are the security risks associated with OpenID?</p>

OpenID is inherently insecure. It works by your site redirecting the user to their open ID provider site and then accepting an ID back from that site. This provides insecurities in both directions. You have to trust the ID that comes back (as you have no way of authenticating the user yourself) and it is easy to operate a proxy to the user’s open ID provider, that allows you to steal their username and password.
OpenID is fine for something like Stack Overflow, where it doesn’t really matter if someone impersonates you. Using OpenID for sites with more serious – on a personal level – content is extremely risky. If you use OpenID for your email for example, then anyone stealing your Id can access your email. They could then in turn send password reminder requests to other sites that you use in order to get passwords for those sites. In the worst case, you could use OpenID for a bank account, or have a bank that sends password reminders to your email account...
There are numerous other security problems with OpenID. You can find more information in
"Privacy on the Internet"
.