this
background:url(http://url);
this
background:url("http://url");
or this
background:url('http://url');
The URL bits of all three of your examples are valid CSS, according to the CSS specification.
Note that the spec identifies some characters in a URL which will need to be escaped with a backslash if present in an unquoted URI, such as parentheses, commas, white space characters, single quotes (') and double quotes (").
For this reason, you might find it better to use single or double quotes around your URLs.
Note that you need to write your full CSS property in the format:
background: url( http://example.com );