Warning: this post is old and might not reflect the current state of the art

Autofocus

<input autofocus="autofocus" /> will put the focus on the specified HTML element when the page loads

Downloading files

<a href="file.pdf" download="pdf-file">Download</a> will download the specified file, with the name provided.

Hide elements

<div hidden="hidden"></div> despite putting the presentation in the HTML, which is bad, this can sometimes turn out useful.

Turning off (or on) spellchecking

Operating systems configured to spell check everything a user types can sometimes get in the way - <input type="text" spellcheck="true|false"> can help.

Auto suggestion text input control

<input list="mylist" name="mylist" />
<datalist id="mylist">
  <option value="CSS"></option>
  <option value="HTML"></option>
  <option value="PHP"></option>
  <option value="Jquery"></option>
  <option value="Wordpress"></option>
</datalist>