It really depends, though. Some games are classic, and you can afford to miss them... but some games, despite awesome reviews and great reception upon realease, die faster as time goes by.
Take, for example, Super Metroid. Still a wicked game, even though it's ancient. I play that sucker usually once a year and still enjoy it (thanks in large part to my never-using-walkthroughs or guides policy) and I don't find anything in the game atrocious. Cave story, same thing. The graphics are simple, work, and haven't necessarily been madly surpassed by anything. The gameplay is still solid, the music still fits... it all just works.
Now, I've gone through my life having played two Final Fantasy games. Those two would be Final Fantasy 6 (SNES) and FFX (Playstation2?). Any time I talk to a FF fanboy, they scream and vouch for FF7, as it's the best RPG in the world etcetera etcetera etcetera. A few months ago, I actually got my hands on a copy of FF7 and gave it a go.
It looks terrible (The enemies... explode? into a mess of broken triangles???), it sounds terrible(The sound made when enemies explode??), and I couldn't get past those two facts long enough to enjoy the story or gameplay. It wasn't the legend I was told it was simply because I was waay late on that train and have seen what can be. It's not that FF7 is or was a crappy game, so no fanboys diving down my throat, please. I just can't stand it because I can't relate to the restrictions of the time.
I also never played Katamari Damacy. If I wait too much longer, I betcha it'll lose its appeal.