Not all the browsers implement HTML in the same way. Some tags pertain to only one browser. What looks good in the browser of your choice may be unreadable in a different browser. Not supporting a browser can cause millions of people to not be able to see your site.
Some browsers are more forgiving than others.
You trust your browser. Let's face the fact that the Web is going commercial. Most Web Designers are designing pages for corporate or business clients. Anything that could adversely affect a large chunk of your target audience is worth looking into and avoiding. Validating your HTML can help to ensure that there are no nasty surprises waiting to grab you or your client unawares.