An image is worth a thousand words… so I got 2 thousand words (Plus change) right here:

1. Select in the Menu: Format → Cells…

   
   
   

   




2. Select in the Format Cells window: Alignment Tab

   
   
   

   




3. Select Wrap Text Automatically from the Properties section.

   
   
   

   The end result will be something similar to this:

   
   
   

   

Note that, at least up to LibreOffice 4.0, this option only works on cells that I written in after the option is activated. It will not automatically wrap cells created before.¹ See the following image:

The cell above was written before the option was activated. The bottom cell was written after the option was activated.

¹ For those wanting to wrap all of their already existing cells in a spreadsheet, simply execute Ctrl+A, following by Ctrl+C, and finally Ctrl+V.