I'd like to talk about web standards in the future, but I realised I need to first define what it is I'm talking about. So, this is what I mean by using 'web standards':
Make sure your HTML and CSS validate.
The point is simple: if you're using a standard format, use it correctly. However, just because your page is valid doesn't mean it's perfect. For this, the W3C's HTML Validator and CSS Validator are your best friends.
Separate the design from the content.
Use CSS to describe how things should look (fonts, colours, widths and heights, borders, etc.) Also, take as many images as you can out of the HTML. Don't use images to display text. Ideally, put all the CSS in an external file, but it's up to you how you organise your code. Just be aware of the tradeoffs.
Separate behaviour from the content.
Use HTML the way it was intended.
By this I'm talking about using HTML semantically. Don't use tables unless you're showing spreadsheet data. Use h1-h6 tags for the headers on your page. Use blockquote only when you're quoting, not for the indentation. Just try to use the full range of HTML tags when appropriate. Sometimes you simply need to use divs and spans, but avoid catching Divitis.
Make your site accessible.
Accessibility is a very important standard, in some places it's actually the law. If you've already taken care of the last four points, chances are your site is already very accessible. Grab an accessibility checklist, and take look at your web site through the eyes and ears of all potential visitors. What does the site sound like with a screen reader? What happens when you increase the font size? Are you using any terminology without giving definitions? This is a big topic, but it often gets forgotten.
This is what I mean by 'web standards'. These are all just guidelines, and there are obvious exceptions to every rule. Next, I'll go into the benefits of following these rules.
Update: I've chosen to go with the term 'Best Practices' to describe what I've discussed here, of which 'web standards' are only a subset. Read my discussion here.