[javascript] Focus Next Element In Tab Index

Tabbable is a small JS package that gives you a list of all tabbable elements in tab order. So you could find your element within that list, then focus on the next list entry.

The package correctly handles the complicated edge cases mentioned in other answers (e.g., no ancestor can be display: none). And it doesn't depend on jQuery!

As of this writing (version 1.1.1), it has the caveats that it doesn't support IE8, and that browser bugs prevent it from handling contenteditable correctly.