Opening tags are required, closing tags are only needed if you have other code (HTML, CSS) after them in the same file. See PHP manual.
A closing tag with nothing after it may lead to problems with included files if they contain a BOM. That’s one of the reasons why all optional closing tags were removed for WordPress 3.4 in core files. Follow this style. It’s useful.
Here is an example from Automattic’s _s theme’s functions.php.