Let the old ones die and attend their funeral
The web is overburdened with old sites, visited by nobody and victims of the pride of their creators, who don’t want to let them go. “It costs nothing”, they say, “and someone may want to read my opinion on carrot soup someday”.
What with the old ones in real life
In real life, the old ones are visited regularly by the members of their family, so that they don’t get forgotten. It’s like a child’s duty to pay a visit every once in a while to grandparents, old uncles and sick elderly aunt Tatiana. Until they die, and then you go to the funeral, gather with the nearest and dearest, cry a little, drink a lot, and start something else.
The same applies to the web
To avoid overpopulation, the web should follow the example given by the family traditions. Any forgotten website for more than, say, a year, should be declared sick, and its creators/members/users/trackbacks should be told about the situation. They could all meet in the website’s backyard on Sundays, to talk about the good old times when the website was still active, and about the Superbowl. That way, the website’s visits figures, although low, would keep at an acceptable level.
Then the web doctor would visit the old website and check its health. He would advise against useless attempts to rejuvenation, give a few coins to the host so that the website doesn’t get kicked out, check that it still looks acceptable on modern browsers… Web doctor could be a nice profession, and if it’s like in real life, it would pay well.
Web funerals
Anyway. After numerous years of brave resistance of the patient, the web doctor could declare it dead. He would call the relatives and ask them to organize the ceremony. A chat would be organized in a #funeral IRC channel, people would overdress and exchange memories of the website, only to say that it was better in the old times, nowadays everything gets corrupted. The creator would choose a picture of the website, and put it on a virtual grave at graveyard.com. Then the host would be informed to wipe out all data, the search indexes would be told to do the same, and the website would only live in our memories, for the best.
How would that change the web?
I see numerous advantages to the old websites dying.
First of all, it leaves room for the youth. Yeah, altavista.com was a kick-ass site, but it’s time to start using a real search engine.
Also, it forces us to keep the knowledge of the past, and is a good way to avoid repeating the same mistakes. The numerous web 2.0 sites coming out everyday have a strange aftertaste of the 00s Internet bubble (unreasonnable cash burn rate, ridiculous business potential).
New sites respect the older ones, and don’t try to show off too much, even if they do better.
The growth rate of the web… well, this will probably not get better.
Your name can’t be found related to some old story anymore. You know, when you wrote in a webmaster forum that JavaScript is crap.
Has-been website creators pass to something else (at last).
Information gathered from websites isn’t outdated in fifty percent of the cases.
Hard disk manufacturers don’t get rich so fast.
And most of all, my searches in Google would return relevant results.

How do you envision something like this occurring from a business standpoint? I’m supporting a fairly large number of sites that I wish would either go away or, even better, I could get paid to redo and modernize.
I’ve never thought of a good way convince a client that something that they paid a lot for a while back is now outdated and could reflect poorly on them. This applies mostly sites I’ve inherited, but I’ll admit I did some real stinkers back in the late ’90s.
An even bigger concern is older applications… Those monolith piles of code that could be rewritten faster than the original could be prototyped, and probably save a lot of hairs on people’s heads with improved usability, but someone has to pay for it.
I’m all in favor of old and irrelevant sites going away, but we developers are the people that need to encourage it.
How do we do that?
Erestar: How about a rule (a law?) making it compulsory to pay a periodical fee (a rent?) inversely proportional to the activity of a site? That would be a good motivation to close never-visited websites.
i don’t quite agree, i still want to be able to access websites of music bands, graphists that don’t exist anymore. What they produced does not loses its value as time passes.
Old websites don’t die, they get archived
That’s not quite like a funeral and burial. More like retirement. You know, leave your position (URL) and allow the younger employees to take over the organization (remove the old guys from live search engines). However, this way we can still give the old websites a call once in a while to reminisce about the old days or, more importantly, to ask where they left file X or why employee Y made decision Z once long ago.
I agree. Websites should die.
I agree if the site is outdated and no longer relevant like a site titled “top 10 gifts for Christmas 1991″ Then you need to update or get rid of it.