I have a site where I used a floated image inside a div element. I wanted the image to appear slightly above the container (while having the text in the container wrap around the bottom of the image) so I have used a negative top margin on the floater...

<div class="text">
    <p><img src="images/round-float-home.png" width="200" height="200" class="floater" />Lorem ipsum dolor sit amet, consectetuer adipiscing elit.</p>
</div>

and from the css file..

.floater {
    float: left;
    margin-top: -125px;
    margin-right: 25px;
    margin-bottom: 5px;
}

By moving the floater up like this, I intended to have it overlap the previous div that was higher up on the page. It works correctly on Firefox 2 & 3, Opera 6, IE7 and Safari on OSX. If you look at it on IE6 the portion of the floated image that is above the containing float has moved "behind" the background image of the above div.

You can see the site at http://test.zeidelicious.com/index2.html

Is there any way to force floats to move "forward" in IE6, sort of analogously to the was Z-index works?

IE6 has major problems with absolute positioning. The problem stems from your absolute positioning on #logo and the positioned divs inside it. I don't see why you need all that positioning either.

It's NOT the float that's the problem here. Get rid of the positioning and use the document flow to your advantage.

Setting #floater to position:relative will get the image on top, but you wouldn't necessarily need it if you didn't have all those absolutes.

position: relative fixed the issue for me... But what is the stylistic faux-pas of using absolutes? I know I use them because they are easy to work with; absolute elements tend to behave more predictably across browsers than what I have experienced with relative elements. I realize that this is my own shortcoming and if I understood CSS better I'm sure everything would seem to behave predictably -- but if I am going to try and learn more about stylesheets I would like to know the benefit over what I have been making use of thus far.

It's not stylistic, it's IE's BUGS that are the issue with absolutes:

http://www.positioniseverything.net/posbugs.html
http://www.positioniseverything.net/abs_relbugs.html

Using all absolutes is just not the best way to do a layout, although there are some who do nothing else - and I don't envy them one bit. I only use positioning in very particular situations in a layout, other than that, I don't need them and I have no problems controlling my layouts cross-browser