It's not as straightforward as it seems though. Yes, all consumer BD players can play regular DVDs and most of them can play CDs. However, they deliberately have to build this capability in, including a separate laser pickup in some cases (the blue laser won't work properly for regular DVD). DVD compatibility is absolutely NOT required but manufacturers know that it is suicide if they don't include support for regular DVD.
One benefit of playing DVDs with BD and even HD-DVD players is that they will upconvert the DVDs to HD quality and output them over HDMI which gives you a cleaner signal. My HD DVD player now makes an excellent upconversion DVD player.
By the way I said "most" can play CDs. There were a few in 2006 or thereabouts that could not play CDs.