Does OpenID improve the user experience?
Edit
Not to detract from the other comments, but I got one really good reply below that outlined 3
Always keep things consistent. OpenID is still in infancy and non-existent to most casual users. It will confuse users who are not familiar with it and they may even end up thinking that they're opting to 'Open' their IDs to the general public.
You can optionally embed a unobtrusive link on the sign up saying "Have an Open ID?". This way you, those familiar with it know to use it, those who aren't simply ignore it.
I ran across this discussion about what's wrong with OpenID and thought it helpful and relevant: http://www.quora.com/What-s-wrong-with-OpenID
I respect your need for a business reason to use OpenID rather than a tech-geeky reason. So here it is:
Reason #1
OpenID is way easier than username+password. "Oh no", I hear the responses now, "OpenID is confusing and scary for users. They'll run away." That's why you don't tell the user it's OpenID. Just offer Yahoo and Google buttons and say "use an account you already have" or something to that effect. Users will love you. Underneath you're using OpenID, but don't advertise the fact, and perhaps don't even offer an OpenID text field, until OpenID becomes more mainstream.
A strong majority of users are already logged into Yahoo or Google, so "Click here to log in using your Google/Yahoo account" buttons will mean it's faster and easier for your customers -> more sales.
Reason #2
Do it for your customers, even if they're not asking for OpenID. OpenID is more secure than username+password, since your customers won't be reusing the same username+password on your site as all their other sites. It's bad security to reuse username+password across web sites, but that's what users do. Using OpenID (without telling them) to get them to reuse their existing [pick your small list of major OPs here] accounts will mitigate this and give your users added security. If your site is hacked, their credentials won't be stolen. And if other sites your customers have accounts with are hacked, there's a good chance your customers account with you won't be compromised.
Reason #3
Fewer support calls and web pages to support users who forgot their passwords.
In my latest application I give the users a choice. I think if you do offer OpenID it should be optional and the fact that it's optional needs be very clear to your users. I tested my signup with "average" users and they were very hesitant to sign in with their Yahoo, Facebook, Google, or what have you.
For users that do want to use OpenID, do it right. If there is additional information that your site requires and you can pull that info in along with their authentication token then do it.
I'm a developer and tech-savvy person and I find it horrible to use OpenID. But that's just my opinion. In the end you have to choose what fits best with your hypothetical end user.
I feel it depends on the end users of your system. Open ID is successful in SO because people who are using SO knows some thing about Open ID.
But, I am not sure whether the same thing will be applicable to a Greeting card site / online shopping site where my parents go. The problem I see here is you give users a choice between various providers they will get confused.
One of the way I could think of for check out process is not to force a user signup. If they decide to simply check out let them do so.