Stacking Divs from Bottom to Top

A more modern answer to this would be to use flexbox.

As with many other modern features, they won't work in legacy browsers, so unless you're ready to ditch support for browsers from the IE8-9 era you will need to look for another method.

Here's how it's done:

.parent {
  display: flex;
  justify-content: flex-end;
  flex-direction: column;
}

.child {
  /* whatever */
}

And that's all you need. For further reading on flexbox, see MDN.

Here's an example of this with some basic styling: http://codepen.io/Mest/pen/Gnbfk

All the answers miss the scrollbar point of your question. And it's a tough one. If you only need this to work for modern browsers and IE 8+ you can use table positioning, vertical-align:bottom and max-height. See MDN for specific browser compatibility.

Demo (vertical-align)

.wrapper {
  display: table-cell;
  vertical-align: bottom;
  height: 200px;
}
.content {
  max-height: 200px;
  overflow: auto;
}

html

<div class="wrapper">
  <div class="content">
     <div>row 1</div>
     <div>row 2</div>
     <div>row 3</div>  
  </div>
</div>  

---

Other than that, I think it's not possible with CSS only. You can make elements stick to the bottom of their container with position:absolute, but it'll take them out of the flow. As a result they won't stretch and make the container to be scrollable.

Demo (position-absolute)

.wrapper {
  position: relative;
  height: 200px;
}
.content {
  position: absolute;
  bottom: 0;
  width: 100%;
}