The other forms are there for compatibility with XHTML; to make it possible to write the same code as XHTML, and have it also work as HTML. Some systems that generate HTML may be based on XML generators, and thus not have the ability to output just a bare <br> tag; if you're using such a system, it's fine to use <br/>, it's just not necessary if you don't need to do it.
Very few people actually use XHTML, however. You need to serve your content as application/xhtml+xml for it to be interpreted as XHTML, and that will not work in IE (it will also mean that any small error you make will prevent your page from being displayed, in browsers that do support XHTML). So, most of what looks like XHTML on the web is actually being served, and interpreted, as HTML. See Serving XHTML as text/html Considered Harmful for some more information.
