Age doesn't matter to me, but I can acknowledge that some old games are pretty shitty. Wolfenstein games, for instance, are awful, the controls are terrible, and the graphics make it a mess, where a potted plant looks the same as a Nazi (blue vase, blue boots, brown leaves, brown uniform). I still find it fun, but I can see how others who didn't play it back when it was new would think it's trash.
However, since this is an opinion on whether I care about age, the answer is certainly no. I adore Ocarina of Time, Donkey Kong Country, Goldeneye, Starfox 64, Actraiser, Splatterhouse, Sonic the Hedgehog (only his Genesis titles), etc. They were great when they came out, and they're great fun now.