Just so that it’s 100% clear for everyone, the W3C HTML5 spec explicitly states that either syntax is fine. (At least, as of January 2019, anyway)
From the spec:
In HTML, these elements have a start tag only. The self-closing tag syntax may be used.
A Self-closing tag is a special form of start tag with a slash immediately before the closing right angle bracket. These indicate that the element is to be closed immediately, and has no content.
In both HTML and XHTML, within each tag, whitespace is permitted after the tag name…Some authors choose to include a space before the slash in the self-closing tag.
So according to the W3C,
<br>, <br/>, and <br /> are all valid HTML. You’re free to use whichever you prefer.
Personally, I prefer all of my tags to close. It feels more consistent, to me. It bugs me to see sporadic unclosed tags throughout a document full of otherwise closed tags. I understand that not everyone shares my phobia, though.
So, by all means, omit the slash if that’s your preference. But it’s perfectly valid to include it if you want to.