EverQuest and Ultima Online, both considered the twin pillars which started the modern MMO genre proper, are both alive and well several years later. While they're not perpetual, they're also fairly robust in their lifespans.
Of course, just because the game isn't dead doesn't mean it's not on life support. Anyone who has played during Final Fantasy XI's glory days will be quick to point out how much more empty the game has gotten in recent years. Graphics advance, and minor improvements seem increasingly minor as time goes by -- City of Heroes is due for an upgrade with its next expansion, but that will only put a new coat of paint on an engine that is several years old now.
How well is your favorite game aging? Does it still look pretty good despite its age, or is it showing definite signs of how long the whole thing has been running? Is it a minor hiccup, or does it make things much less enjoyable, even to the point of being unplayable?