Five or ten years from now, when everyone has next gen DVD machines, that allow for HD etc., will they play old fashioned single and dual layer DVDs no problem? I presume they will? Is it safe to think that?

Both blu-ray and HD-DVD player manufacturers have indicated that all their
players will be backwords compatible (CD, DVD, VideoCD(?)), so that will be
no problem at all (otherwise sales would hurt).

After that would be anyone's guess. But since DVD has a very high market
penetration I would not be suprised if the next standard will either support
it or come with dual player drives (a bit like the VHS / DVD in-one players
that are out there now).