As a career path, the web has one great advantage over all others - it’s publicly accessible. You can demonstrate your skills and allow everyone to view them, at any time.
If you’re going to do this, be ready to push your skills to the limit. Refine the code, over and over. Use validators like those at http://w3c.org, and tools like http://websiteoptimization.com to check your work. Test with different browsers.
If you’re using commercial, open source products, go to those sites and view some sites built with them. See what other people are doing. View their code to learn more. Join the forum, to both get help and contribute.
Be honest, if you’re an engineer, state that, and if you’re a designer say so. Most people aren’t experts in every skill required to deliver a great site.
Invest in a domain name and use it. Keep it professional. You can always create a subdomain or buy another domain to put fun stuff up.
If you are a recruiter or HR person and you receive a resume for a web position that doesn’t include sample URLs, ask for them and have your web team review them. You will have a chance to evaluate a candidate’s work before you ever speak to them. Check the copyright dates to ensure you’re looking at recent work.