[Peroni]

>How do I convince potential employers to judge me based on my actual experience and code, rather than contrived coding exercises over Skype?

Consider the person who has the final say in the process. Be it the CTO, CEO, founder, et al. Committing to hiring someone is a big deal. They are taking a risk. Ultimately, it's near impossible to be 100% certain of a persons suitability until they are actually performing in the role itself.

When they are coming to a decision as to whether or not they should hire Candidate X, one of the questions they need answered is "Is this person technically capable". They need something to eliminate that question and all too often they rely on their team asking you to reverse a string or something to that effect.

To answer your actual question, it's important to avoid sounding arrogant but I sincerely suggest you pose your argument as succinctly as you have in your post above and run a mile if you get any objections.

[devplusplus]

Yes. I don't disagree. Hiring someone is super important, and paying me is very expensive. I don't disagree that they need to be as certain as possible regarding my technical skills. I just need to figure out a way, when asked to reverse a string or what-not, to say "Look, this is Programming 101 stuff, and if you really want to know what I'm capable of, let's look at some projects I've worked on in the past" without coming across as arrogant. (I don't think it's arrogance -- I just think it's not representative of my skill level and experience.)

[Peroni]

Address the issue before it comes up. During the initial phone/email conversations where they are suggesting you participate in their interview process, ask them there and then how they assess technical suitability. That's your opportunity to raise your concerns.