Probably one of the least respected languages of all time, HTML is ironically consumed by virtually every human being who boots up a computer each day. But at the same time, if you are trying to attract visitors to your site via organic search, SEO matters... a lot. The Semantic Web becomes more important each day. When I develop web sites, I make this a top-priority. If your budget does not allow for this, I'll likely pass on the project.
The list of features that are part of or associated with the HTML5 specification is long and impressive. There are of course issues with which browsers support which features (and how they support them) but with a little careful planning, a graceful degradation path can be worked out.
For the first 10 years of the internet age, it was all about having a web site; just having your own domain and a decent-looking set of pages was enough. In later years, everyone wanted animated GIFs, and Flash, then AJAX. Many folks were not really sure whey they needed these technologies implemented (and often they really didn't it), they just knew that the neighbors had 'em.
Now everyone wants a mobile web site. The difference here is: it's a really good idea. If you have a web site, more and more visitors are consuming it with some kind of tablet or mobile device each day. Addressing this growing trend is simply good business. I can create a mobile-specific site for you, using a light-weight tool such as jQuery Mobile, or I can optimize your existing site so that it looks stunning across all devices via a technique called "Responsive Design" (if you are not sure what that is, re-size your browser right now, and as you make it as narrow as possible, you will see the design of the page react to the amount of available screen space, and adjust....likewise when you make your browser wider and wider).