Using HTML as Intended
Despite what HTML has become, it was never intended to be used to design web pages, but rather give structure to documents. Perhaps one of the reasons why it was adopted for design is because it would make browsers display text differently depending on the tags that surrounded it. As more and more design hacks circulated, proper use of the tags was no longer necessary to achieve the same effect. This has resulted in the use of HTML code that does not reflect the structure of the document that it is displaying.
Part of the reason that HTML has become so "misused" is that there were little alternatives available to solve the design problems of the time. Cascading Style Sheets (CSS) were still new and not supported enough to be relied upon for page display, and so HTML tricks were developed as work-arounds. Now that style sheets much better supported, the time has come for us to unlearn those HTML tricks and use HTML as it was intended. It might not be easy at first, but it is certainly something that I feel is worth doing.
The Importance of HTML Structure
I know what you may be thinking, there is little point in rewriting the HTML if the page looks just fine as it is, right? While it may look just fine to your regular visitors, it could be a nightmare for anyone that needs to follow the page without seeing it.
So who would I be referring to exactly? Well, there are those that rely on a speech browser to read the page to them; they would find a page built with lots of nested tables difficult to follow at the best of times. Perhaps the most influential visitor that comes to your site is the search engine spider, all they see is the HTML code, and if they can't work out which words are important then how can they give you a good ranking?
The logical use of HTML is getting increasingly important, particularly when it comes to the search engines ability to understand a search word in relation to your page. Making proper use of HTML not only makes your web pages "cleaner" and thus more readable to anyone viewing your code, but it also helps you to separate your content from your design and so improves the ability for you or anyone else to maintain your site.
Making your HTML more Logical
You don't need to do too much to make any new pages that you create more search engine friendly. Just remember to use HTML as it was intended. If you are using text as a header, put it in a header tag; don't forget to put your most important header in a H1 tag and work your way down from there. If you want to display text as a list, use the appropriate list tags as opposed to a HTML table.
Don't be tempted to use the old HTML tricks that were developed as workarounds to stylistic problems; most layouts are achievable with a little knowledge of style sheets and a bit of time for trial and error. CSS is great for making various tags such as headers and lists behave the way you want to. Text in a list doesn't have to be displayed as a list, nor does it need to be indented or use bullets. Take a look at the links at the very top of my pages here at Web Site Owner. You couldn't tell just by looking at it that I've used an unordered list there!
One other reason why it might be a good idea for you to take a fresh look at your HTML is to prepare your site for the future. Current browsers, particularly Internet Explorer, are rather forgiving of any mistakes that you make in your HTML code. However, as the webmasters dream of having a single set standard to follow becomes ever more likely, the chances are the browsers will become much more stricter in the way that they render their pages. If this happens and nothing is done to prepare for it, then some pages on the web will certainly become unusable.
Checking your code now will make sure that your site is still viewable for the foreseeable future. It also gives you a chance to review any pages on your site that might be out of date!