Align two inline-blocks left and right on same line

For both elements use

display: inline-block;

the for the 'nav' element use

float: right;

Edit: 3 years has passed since I answered this question and I guess a more modern solution is needed, although the current one does the thing :)

1.Flexbox

It's by far the shortest and most flexible. Apply display: flex; to the parent container and adjust the placement of its children by justify-content: space-between; like this:

.header {
    display: flex;
    justify-content: space-between;
}

Can be seen online here - http://jsfiddle.net/skip405/NfeVh/1073/

Note however that flexbox support is IE10 and newer. If you need to support IE 9 or older, use the following solution:

2.You can use the text-align: justify technique here.

.header {
    background: #ccc; 
    text-align: justify; 

    /* ie 7*/  
    *width: 100%;  
    *-ms-text-justify: distribute-all-lines;
    *text-justify: distribute-all-lines;
}
 .header:after{
    content: '';
    display: inline-block;
    width: 100%;
    height: 0;
    font-size:0;
    line-height:0;
}

h1 {
    display: inline-block;
    margin-top: 0.321em; 

    /* ie 7*/ 
    *display: inline;
    *zoom: 1;
    *text-align: left; 
}

.nav {
    display: inline-block;
    vertical-align: baseline; 

    /* ie 7*/
    *display: inline;
    *zoom:1;
    *text-align: right;
}

The working example can be seen here: http://jsfiddle.net/skip405/NfeVh/4/. This code works from IE7 and above

If inline-block elements in HTML are not separated with space, this solution won't work - see example http://jsfiddle.net/NfeVh/1408/ . This might be a case when you insert content with Javascript.

If we don't care about IE7 simply omit the star-hack properties. The working example using your markup is here - http://jsfiddle.net/skip405/NfeVh/5/. I just added the header:after part and justified the content.

In order to solve the issue of the extra space that is inserted with the after pseudo-element one can do a trick of setting the font-size to 0 for the parent element and resetting it back to say 14px for the child elements. The working example of this trick can be seen here: http://jsfiddle.net/skip405/NfeVh/326/

Taking advantage of @skip405's answer, I've made a Sass mixin for it:

@mixin inline-block-lr($container,$left,$right){
    #{$container}{        
        text-align: justify; 

        &:after{
            content: '';
            display: inline-block;
            width: 100%;
            height: 0;
            font-size:0;
            line-height:0;
        }
    }

    #{$left} {
        display: inline-block;
        vertical-align: middle; 
    }

    #{$right} {
        display: inline-block;
        vertical-align: middle; 
    }
}

It accepts 3 parameters. The container, the left and the right element. For example, to fit the question, you could use it like this:

@include inline-block-lr('header', 'h1', 'nav');

If you don't want to use floats, you're going to have to wrap your nav:

<header>
<h1>Title</h1>
<div id="navWrap">
<nav>
    <a>A Link</a>
    <a>Another Link</a>
    <a>A Third Link</a>
</nav>
</div>
</header>

...and add some more specific css:

header {
//text-align: center; // will set in js when the nav overflows (i think)
width:960px;/*Change as needed*/
height:75px;/*Change as needed*/
}

h1 {
display: inline-block;
margin-top: 0.321em;
}

#navWrap{
position:absolute;
top:50px; /*Change as needed*/
right:0;
}

nav {
display: inline-block;
vertical-align: baseline;
}

You may need to do a little more, but that's a start.