Using invalid markup like your example can cause unexpected behavior in different pages. If you use valid markup, browsers will (or should) display your content based on the spec. But if you use invalid markup, the browser will try and interperet the markup and display the page how it thinks you meant it to be. Sometimes they will display it how you want, sometimes not. Here's an example from Firefox 3.5 on a Mac.
The first list is your code, but with the proper <ul>
tag replacing the <div>
tag. The second list is your code exactly. Notice that the second list is missing the default margins on the left and bullets.
Basically, nothing will die if you use invalid markup like this, but it's really bad practice since it will lead to unexpected and inconsistent results.