Some advantages of having a portfolio site:
- Pictures vs. words: you can show what you've done rather than having to explain it in text
- Volume: you can include as many sites as you like, organizing them so that they are easy to find, without packing them all onto a single page
- Preservation: if you've done some work on a site that has since been redone, you can point to the work that you did (especially important if the new site is worse)
Keep in mind that in some cases, you may be limited with respect to what you can post on your site (if you worked on sites that are not publicly accessible, for example). If your work is primarily or exclusively on private sites, then you may want to consider creating a small, public site yourself, simply to demonstrate the same skills you used on the sites you can't display.
If you don't have a portfolio site, then you're going to have to have some kind of hook in your resume or cover letter (or both), something that gives the hiring manager a reason to talk to you. A portfolio site doesn't necessarily prove that you can do the work for which you're applying (it can be faked as easily as anything else on a resume), but without one, you're relying strictly on your words to show what you can do, and that may not be enough.