I don't really think DVD is on its way out. BluRay isn't a replacement -- it's a new high end for "us" (enthusiasts, hobbyists - geeks). The average American, many of whom were still happy with the picture quality of VHS, doesn't care about the difference between 480p and 1080p.
Laserdisc, CED, Betamax, DVHS, HD-DVD, etc. all prove that simply being the technically *best* format isn't enough to inspire massive change. DVD was such a revolution because it was such an enormous leap that it sold itself. So much changed beyond the resolution -- the form factor, the affordability, the ubiquity, the quick cross-platform support... and things like the *way* it was sold and the culture behind it. All that came together in a neat and maybe once-in-a-generational way to convince people to upgrade something that they weren't necessarily unhappy about in the first place.
I like BluRay, I've spent lots of money on it, I'm on my second player now and I have shelves of BluRay movies usually purchased to replace an existing DVD... but I couldn't walk into someone's home and tell them they need to do the same thing instead of keeping what they have or at best buying a much cheaper upconverting DVD player. It's inches instead of miles -- it just doesn't matter (beyond the marketing, which did start off very strong selling it as a 'cool' toy - I think that in and of itself has died a natural death...).
(And in fact, there are some heavy negatives about BluRay right now. My parents have a player and my mom can't stand the load times or the fact that she pays an extra ten dollars for each movie.)
As for streaming... I remember people promising exactly the asme thing when DVD was on the rise. It's a great idea and it sounds awfully futuristic and I bet we've all had some cool experiences playing around with it... but there are some negatives.
One big point is that streaming has actually been around for quite some time -- PPV and On Demand and the like over coax. You didn't use these services. It isn't a technical issue that keeps that in the background - it's the fact that you pay for the viewing or digital ownership and end up with nothing at the end of the day. Similarly, we've had video rental over Xbox Live, Tivo/Amazon, AppleTV, etc. for some years now. It's 'there' but it hasn't caught on as a replacement for DVD.
The fact of the matter is that Hulu and Netflix Streaming and the like are so hip at the moment because they're perceived as being *free*. If somebody can give me access to every movie and TV show ever at some sustainable rate for $20 a month, then I'll be as happy as a clam in sauce... but it isn't going to happen. The need to make a profit will ultimately prevent Future Streaming Service X from being the one sort that has attracted us so far.
(In-person rentals are probably doomed -- but more from the long-lasting effects of Blockbuster's failure to control the DVD market years ago than from some immediate supertech that's blowing our minds.)
It's mainly for a collection of documentaries I have that you can't find on DVD, but every once in a while I need it for something else random. I really don't see any need to eliminate this capability from my awesomest multimedia setup.
The only worry is tape decay. My Wing Commander Academy dubs are pretty brittle after 13 years. If you have anything spectacularly rare you might want to move it over to something digital where it can at least be duplicated/backed up easily.