How do I know if I need a sub woofer?

Besides extending the bottom octave of your system, adding subs will also improve soundstage width and depth. 

There is some spatial information in those very low frequencies.

It is most noticeable in orchestral classical music, but all music will benefit in this aspect.  

The only way to find out is to try one and see if you like it! What speakers are you using?

to hear and FEEL pipe organs as they were meant to be heard and FELT, you need to be able to reproduce cleanly down to about 16 cycles per second. precious few stereo speakers can do that trick. a pair of subs is mandatory for all us pipe organ lovers.

The last few pictures in my virtual system demonstrate how multiple subwoofers not only extend the low end response but also reduce room modes and concomitant ringing. This is objective. There are subjective improvements in depth and soundstage as well. 

I listen at low volumes late at night---if I want a little more bass, I use the loudness on my integrated. I will say that I did have a REL sub and sold it since I didn't use most of the time. But now I miss it.