Keep a Web site as a backup, that's not a bad idea. But don't use that Web site as your primary portfolio.
Also, a word about presentation. When I started sending out portfolios during the months leading up to my graduation, I took a flimsy black binder and stuffed the cover letter on the left and the stories, which were paperclipped, on the right. During that stretch, I applied to about 50 newspapers of varying sizes and never heard back from one.
Then I decided to spend a little more money. I bought black binders, nice ones with the plastic on the front, and plastic filler pages. I stuffed the cover letter on -- gasp! -- the binder's cover, then inserted my stories in the filler pages. It looked a heck of a lot better and, within the first month of this change, I received three phone calls, two interviews and one job offer. I took the job.
Were my stories good before? Sure, but the presentation sucked. Make sure editors know how good your stuff is -- and make sure it's easy on the eyes. Presentation likely will never be the deciding factor, but it doesn't hurt. (That said, don't go overboard.)