Sometimes bringing your site more current is as simple as adding some fresh content and archiving the old, while other times you may be getting due for a redesign or complete overhaul. Have some friends or colleagues look at your site for you and ask them for honest critiques. Sometimes we can't see the forest for the trees, so to speak, so asking others to take a look can bring a different, fresh perspective. Ask them if your site is easy to navigate, if they find any dead links, if the content is helpful and interesting, and if they have any ideas that might improve your site. You can gain so much fabulous information or ask for a critique of your site if you wish.
New browsers continue to come out.
Make sure your code is up to date and that it continues to work fine in the latest browsers and platforms. Your usage logs can usually tell you the browsers, platforms, and versions used by your visitors. Generally speaking, your site probably needs to work fine from at least versions 4 and up of the two major browsers, Netscape and Internet Explorer, for both Macs and PCs. Netscape 6 recently came out, and there may be some surprises with how your site works. So it's important to check it out and make sure your site renders OK in it, too.