First off, congrats on having a Web site with longevity! Seems like most people were in a completely different industry eight years ago. :-)
The key question you ask is are FRAMES deprecated in the latest version of HTML?
According to the standards body that defines the HTML language (w3.org, the latest version of HTML, HTML 4.01, does include frames, without stating that it's deprecated or obsolete. So that's good. You should be in the clear in terms of your site working in newer browsers as things continue to evolve.
However, there's a bigger question, which is "can you get by with an old site design"?
For most people, the answer is no, you cannot. Everything keeps changing and evolving and whether it's your online business or just a hobby, if you want to stay relevant and attractive to your visitors, you probably need a redesign built around CSS and more modern design.
Now, having said that, realize that if you implement it properly, you should only have to go through the pain of rebuilding your site once. What makes this workable is that you have all of your Cascading Style Sheet (CSS) information in a single shared file and reference it in all your separate files.
Indeed, I have written a specific blog entry here on my site about how to link to external style sheets too, since the syntax is a wee bit tricky.
And, finally, if I may, I have a book that you might find useful, Creating Cool Web Sites with HTML, XHTML and CSS. I talk a lot about CSS and how to migrate from older HTML designs to more fancy CSS designs.
Hope that's helpful!
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I would agree that you should "bite the bullet" and take the time to switch to CSS, even if you are still going to use frames.
I recently redesigned our website to switch from our "old" 1990's-style site, to a more modern CSS style. I kept the content >90% the same, but I now have a single file for the page headings, one for the main menu bar, one for the sidebar navigation, and one for the footer. Now, aside from a few lines of server-side includes, the pages are almost pure content, with very little clutter for the stuff that doesn't change from page to page.
While it took a few days (there are probably about 100 pages on the site), any changes are now a breeze, and any changes in style or look are done in one file.