Favicon: .ico or .png / correct tags?

I know this is an old question.

Here's another option - attending to different platform requirements - Source

<link rel='shortcut icon' type='image/vnd.microsoft.icon' href='/favicon.ico'> <!-- IE -->
<link rel='apple-touch-icon' type='image/png' href='/icon.57.png'> <!-- iPhone -->
<link rel='apple-touch-icon' type='image/png' sizes='72x72' href='/icon.72.png'> <!-- iPad -->
<link rel='apple-touch-icon' type='image/png' sizes='114x114' href='/icon.114.png'> <!-- iPhone4 -->
<link rel='icon' type='image/png' href='/icon.114.png'> <!-- Opera Speed Dial, at least 144×114 px -->

This is the broadest approach I have found so far.

Ultimately the decision depends on your own needs. Ask yourself, who is your target audience?

UPDATE May 27, 2018: As expected, time goes by and things change. But there's good news too. I found a tool called Real Favicon Generator that generates all the required lines for the icon to work on all modern browsers and platforms. It doesn't handle backwards compatibility though.

See here: Cross Browser favicon

Thats the way to go:

<link rel="icon" type="image/png" href="http://www.example.com/image.png"><!-- Major Browsers -->
<!--[if IE]><link rel="SHORTCUT ICON" href="http://www.example.com/alternateimage.ico"/><![endif]--><!-- Internet Explorer-->

For compatibility with all browsers stick with .ico.

.png is getting more and more support though as it is easier to create using multiple programs.

for .ico

<link rel="shortcut icon" href="http://example.com/myicon.ico" />

for .png, you need to specify the type

<link rel="icon" type="image/png" href="http://example.com/image.png" />