How do I set the table cell widths to minimum except last column?

This works in Google Chrome, at least. (jsFiddle)

table {
  border: 1px solid green;
  border-collapse: collapse;
  width: 100%;
}

table td {
  border: 1px solid green;
}

table td.shrink {
  white-space: nowrap
}

table td.expand {
  width: 99%
}

<table>
  <tr>
    <td class="shrink">element1</td>
    <td class="shrink">data</td>
    <td class="shrink">junk here</td>
    <td class="expand">last column</td>
  </tr>
  <tr>
    <td class="shrink">elem</td>
    <td class="shrink">more data</td>
    <td class="shrink">other stuff</td>
    <td class="expand">again, last column</td>
  </tr>
  <tr>
    <td class="shrink">more</td>
    <td class="shrink">of </td>
    <td class="shrink">these</td>
    <td class="expand">rows</td>
  </tr>
</table>

Slightly different topic but maybe it helps someone who stumbles on this question like me.
_{(I just saw the comment by Campbeln who suggests exactly this after writing my answer below, so this is basically a detailed explanation of his comment)}

I had the problem the other way around: I wanted to set one table column to the minimum width possible without breaking it on white space (last column in the following example) but the other's width should be dynamic (including line breaks):

-----------------------------------------------------------------------------------
element1 | data      | junk here which can   | last column, minimum width, one line
                       span multiple lines
-----------------------------------------------------------------------------------
elem     | more data | other stuff           | again, last column
-----------------------------------------------------------------------------------
more     | of        | these                 | rows
-----------------------------------------------------------------------------------

Simple solution:

HTML

<table>
  <tr>
    <td>element1</td>
    <td>data</td>
    <td>junk here which can span multiple lines</td>
    <td class="shrink">last column, minimum width, one line</td>
  </tr>
  <tr>
    <td>elem</td>
    <td>more data</td>
    <td>other stuff</td>
    <td class="shrink">again, last column</td>
  </tr>
  <tr>
    <td>more</td>
    <td>of</td>
    <td>these</td>
    <td class="shrink">rows</td>
  </tr>
</table>

CSS

td.shrink {
  white-space: nowrap;
  width: 1px;
}

Columns with class shrink only expand to the minimum width but others stay dynamic. This works because width of td is automatically expanded to fit whole content.

Example Snippet

table {
  width: 100%;
}

td {
  padding: 10px;
}

td.shrink {
  white-space: nowrap;
  width: 1px;
}

<table>
  <tr>
    <td>element1</td>
    <td>data</td>
    <td>junk here which can span multiple lines</td>
    <td class="shrink">last column, minimum width, one line</td>
  </tr>
  <tr>
    <td>elem</td>
    <td>more data</td>
    <td>other stuff</td>
    <td class="shrink">again, last column</td>
  </tr>
  <tr>
    <td>more</td>
    <td>of</td>
    <td>these</td>
    <td class="shrink">rows</td>
  </tr>
</table>

whitespace-wrap: nowrap is not valid css. It's white-space: nowrap you're looking for.

td:not(:last-child){
    white-space: nowrap;
}

td:last-child{
    width: 100%;
}

By using the code above, the last table-cell will try to be as big as possible, and you will prevent the ones before that from wrapping. This does the same as the other answers given, but way more efficient.