How can I transition height: 0; to height: auto; using CSS?

Use max-height in the transition and not height. And set a value on max-height to something bigger than your box will ever get.

See JSFiddle demo provided by Chris Jordan in another answer here.

#menu #list {
    max-height: 0;
    transition: max-height 0.15s ease-out;
    overflow: hidden;
    background: #d5d5d5;
}

#menu:hover #list {
    max-height: 500px;
    transition: max-height 0.25s ease-in;
}
<div id="menu">
    <a>hover me</a>
    <ul id="list">
        <!-- Create a bunch, or not a bunch, of li's to see the timing. -->
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
    </ul>
</div>

The solution that I've always used was to first fade out, then shrink the font-size, padding and margin values. It doesn't look the same as a wipe, but it works without a static height or max-height.

Working example:

/* final display */
#menu #list {
    margin: .5em 1em;
    padding: 1em;
}

/* hide */
#menu:not(:hover) #list {
    font-size: 0;
    margin: 0;
    opacity: 0;
    padding: 0;
    /* fade out, then shrink */
    transition: opacity .25s,
                font-size .5s .25s,
                margin .5s .25s,
                padding .5s .25s;
}

/* reveal */
#menu:hover #list {
    /* unshrink, then fade in */
    transition: font-size .25s,
                margin .25s,
                padding .25s,
                opacity .5s .25s;
}
<div id="menu">
    <b>hover me</b>
    <ul id="list">
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
    </ul>
</div>

<p>Another paragraph...</p>

You should use scaleY instead.

ul {
  background-color: #eee;
  transform: scaleY(0);    
  transform-origin: top;
  transition: transform 0.26s ease;
}
p:hover ~ ul {
  transform: scaleY(1);
}
<p>Hover This</p>
<ul>
  <li>Coffee</li>
  <li>Tea</li>
  <li>Milk</li>
</ul>

I've made a vendor prefixed version of the above code on jsfiddle, and changed your jsfiddle to use scaleY instead of height.

Edit Some people do not like how scaleY transforms the content. If that is a problem then I suggest using clip instead.

ul {
  clip: rect(auto, auto, 0, auto);
  position: absolute;
  margin: -1rem 0;
  padding: .5rem;

  color: white;

  background-color: rgba(0, 0, 0, 0.8);

  transition-property: clip;
  transition-duration: 0.5s;
  transition-timing-function: cubic-bezier(0.175, 0.885, 0.32, 1.275);
}
h3:hover ~ ul,
h3:active ~ ul,
ul:hover {
  clip: rect(auto, auto, 10rem, auto);
}
<h3>Hover here</h3>
<ul>
  <li>This list</li>
  <li>is clipped.</li>
  <li>A clip transition</li>
  <li>will show it</li>
</ul>
<p>
  Some text...
</p>

You can't currently animate on height when one of the heights involved is auto, you have to set two explicit heights.