I always thought that when you talked in general, you never used the definite article 'the'. However I have heard 'he plays the piano' instead of 'he plays piano' a lot of times. In fact, I remember a song that says: "We sing and we dance when we play the drum...".
From the other thread (please do read it before commenting here) you'll see a suggestion that it makes a difference if you include a modifier before guitar - as in this case.
So although I play the guitar (with article), I also happily play bass guitar (no article).
That's a long thread! How about this?
I play the guitar = this is my hobby/profession.
I play guitar in the band = this is my role in the band.
EDIT: I see Panj's point. "I play the bass guitar" sounds a little odd in either case. If we specify the type of guitar we tend to avoid the article.
It doesn't matter, and doesn't depend on whether you speak AE or BE. Here we say "Bob plays violin" and they do in the UK as well. Example: David Bowie, as Ziggy Stardust: "Ziggy played.... gui...taaa....aaaaar." You see?