To second what other posters have said, while it is best to upgrade the whole system, sometimes it can't be done all at one time. Of course the only way to benefit from the Blu-Ray quality is to upgrade all the cabling to something that will handle the HD signals (such as HDMI) as well as upgrading all the TV's and AV components to the same standard.
When we upgraded we wanted to keep the old non-HD TV in the bedroom working with the Blu-Ray player up front. We bought a box to convert HDMI to composite video to feed into the original selector box.
Here is an example from Amazon.