Frankly, in a nutshell: Wikipedia should have been using OpenID a long time ago.
Most people already have an OpenID.
Everyone who's anyone has an account with Google, Yahoo!, or AOL. Whether they know it or not, an account with one of these websites can be used as an OpenID. Easy.
It's simple and secure.
No one likes remembering their password for every website they use, and it is very insecure to use the same password for multiple sites (though many do). Where is the balance between password strength and password fatigue? OpenID.
Plus, it facilitates registration.
OpenID made my registration at Stack Overflow ridiculously easy. They practically tricked me into registering! Anonymous IP editing is good, but registered editing is better, and OpenID support would make it that much more appealing.
It's opt-in.
If you don't want to use OpenID to create your account or log in, you don't have to! OpenID can be easily implemented such that its only effect is beneficial.
