Tables are never really properly responsive. However, in the Modern or Bootstrap themes, you can create a div with class "table-responsive" around your table and it will get a horizontal scrollbar on very small screens.

For example, here is a table which should be scrollable sideways on a mobile device.

Entry Header 1Entry Header 2Entry Header 3Entry Header 4
Entry First Line 1 Entry First Line 2 Entry First Line 3 Entry First Line 4
Entry Line 1 Entry Line 2 Entry Line 3 Entry Line 4
Entry Last Line 1 Entry Last Line 2 Entry Last Line 3 Entry Last Line 4

The HTML for this table looks a bit like this:

<div class="table-responsive">
    <table class="table table-striped table-hover">
      ...contents of table...
    </table>
</div>

 See the Bootstrap Documentation for Tables for more information.