As far as I know, basic animates can't animate non-numeric CSS properties.

I believe you could get this done using a step function and the appropriate css3 transform for the users browser. CSS3 transform is a bit tricky to cover all your browsers in (IE6 you need to use the Matrix filter, for instance).

EDIT: here's an example that works in webkit browsers (Chrome, Safari): http://jsfiddle.net/ryleyb/ERRmd/

If you wanted to support IE9 only, you could use transform instead of -webkit-transform, or -moz-transform would support FireFox.

The trick used is to animate a CSS property we don't care about (text-indent) and then use its value in a step function to do the rotation:

$('#foo').animate(
..
step: function(now,fx) {
  $(this).css('-webkit-transform','rotate('+now+'deg)'); 
}
...

Ryley's answer is great, but I have text within the element. In order to rotate the text along with everything else, I used the border-spacing property instead of text-indent.

Also, to clarify a bit, in the element's style, set your initial value:

#foo {
    border-spacing: 0px;
}

Then in the animate chunk, your final value:

$('#foo').animate({  borderSpacing: -90 }, {
    step: function(now,fx) {
      $(this).css('transform','rotate('+now+'deg)');  
    },
    duration:'slow'
},'linear');

In my case, it rotates 90 degrees counter-clockwise.

Here is the live demo.

In my opinion, jQuery's animate is a bit overused, compared to the CSS3 transition, which performs such animation on any 2D or 3D property. Also I'm afraid, that leaving it to the browser and by forgetting the layer called JavaScript could lead to spare CPU juice - specially, when you wish to blast with the animations. Thus, I like to have animations where the style definitions are, since you define functionality with JavaScript. The more presentation you inject into JavaScript, the more problems you'll face later on.

All you have to do is to use addClass to the element you wish to animate, where you set a class that has CSS transition properties. You just "activate" the animation, which stays implemented on the pure presentation layer.

.js

// with jQuery
$("#element").addClass("Animate");

// without jQuery library
document.getElementById("element").className += "Animate";

One could easly remove a class with jQuery, or remove a class without library.

.css

#element{
    color      : white;
}

#element.Animate{
    transition        : .4s linear;
    color             : red;
    /** 
     * Not that ugly as the JavaScript approach.
     * Easy to maintain, the most portable solution.
     */
    -webkit-transform : rotate(90deg);
}

.html

<span id="element">
    Text
</span>

This is a fast and convenient solution for most use cases.

I also use this when I want to implement a different styling (alternative CSS properties), and wish to change the style on-the-fly with a global .5s animation. I add a new class to the BODY, while having alternative CSS in a form like this:

.js

$("BODY").addClass("Alternative");

.css

BODY.Alternative #element{
    color      : blue;
    transition : .5s linear;
}

This way you can apply different styling with animations, without loading different CSS files. You only involve JavaScript to set a class.