This was bugging me too, since this was a standard feature in Sublime Text 2, but somehow automatic indentation no longer worked in Sublime Text 3 for HTML files.
My solution was to find the Miscellaneous.tmPreferences file from Sublime Text 2 (found under %AppData%/Roaming/Sublime Text 2/Packages/HTML) and copy those settings to the same file for ST3.
Now package handling has been made more difficult for ST3, but luckily you can just add the files to your %AppData%/Roaming/Sublime Text 3/Packages folder and they overwrite default settings in the install directory. Just save this file as "%AppData%/Roaming/Sublime Text 3/Packages/HTML/Miscellaneous.tmPreferences" and auto indent works again like it did in ST2.
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>name</key>
<string>Miscellaneous</string>
<key>scope</key>
<string>text.html</string>
<key>settings</key>
<dict>
<key>decreaseIndentPattern</key>
<string>(?x)
^\s*
(</(?!html)
[A-Za-z0-9]+\b[^>]*>
|-->
|<\?(php)?\s+(else(if)?|end(if|for(each)?|while))
|\}
)</string>
<key>batchDecreaseIndentPattern</key>
<string>(?x)
^\s*
(</(?!html)
[A-Za-z0-9]+\b[^>]*>
|-->
|<\?(php)?\s+(else(if)?|end(if|for(each)?|while))
|\}
)</string>
<key>increaseIndentPattern</key>
<string>(?x)
^\s*
<(?!\?|area|base|br|col|frame|hr|html|img|input|link|meta|param|[^>]*/>)
([A-Za-z0-9]+)(?=\s|>)\b[^>]*>(?!.*</\1>)
|<!--(?!.*-->)
|<\?php.+?\b(if|else(?:if)?|for(?:each)?|while)\b.*:(?!.*end\1)
|\{[^}"']*$
</string>
<key>batchIncreaseIndentPattern</key>
<string>(?x)
^\s*
<(?!\?|area|base|br|col|frame|hr|html|img|input|link|meta|param|[^>]*/>)
([A-Za-z0-9]+)(?=\s|>)\b[^>]*>(?!.*</\1>)
|<!--(?!.*-->)
|<\?php.+?\b(if|else(?:if)?|for(?:each)?|while)\b.*:(?!.*end\1)
|\{[^}"']*$
</string>
<key>bracketIndentNextLinePattern</key>
<string><!DOCTYPE(?!.*>)</string>
</dict>
</dict>
</plist>