I probably have a different attitude to interviews than most because I'm not looking to change the world or aiming to climb some career ladder. I'm just cruising towards retirement. When I'm being interviewed I try to convey a quite confidence that I can do the job as advertised, plus anything else that might come up in the future. Of course this is much easier when you've been around a bit longer than it might be in say the first decade or so of your career.
When I've been the one doing the interviewing I've always dismissed anyone who came across as cocky or arrogant, so I try not to appear so myself. I don't challenge the interviewer in any way, as I see nothing to be gained by doing so. Rather than having him think you're good he's more likely to be offended, which means someone else gets the job.
From my CV they already know what I can do and have achieved, so I don't go over that again unless they want to discuss it. I let them know how I tackle IT and how I think their company will benefit from that approach. Note that this aspect needs to be tailored for the specific job. A small company, such as where I work now, requires a completely different attitude and approach to a large company (my previous job was in Warren Buffett's empire).
I do not tell them, or even imply, that my predecessor had shortcomings unless they raise the subject first. Even then, handle it delicately. If you appear too quick to criticize you've lost them.
For my current job I was interviewed twice. First by what is now my immediate boss to talk tech. I was then asked to come back a few days later to talk with the owner, so that he could decide whether or not he thought we could work well together. That second interview was the more important but I would not have had it had I not satisfied the tech aspect.
Edit: Fixed a couple of typos caused by posting too late at night. :)