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 1||Entry Header 2||Entry Header 3||Entry 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:
<table class="table table-striped table-hover">
...contents of table...
See the Bootstrap Documentation for Tables for more information.