It's a feeling I know all too well. There are some games that everyone tells me are amazing, but that I think are terribly overrated. Halo, Ocarina of Time (in fact, let's just throw Zelda as a franchise in there), and so on. I do try to play classics when I can, and sometimes I play a game that is genuinely excellent and deserves its reputation. Other times, I play a game and wonder why it was ever popular.
The revelation I've taken from doing so is: games do not age well. In fact, games age far more poorly than pretty much any other medium. Citizen Kane will always look imposing and fantastical, the words written in Peter Pan will never be lacking an imagination to enjoy them, but video games have factors that make it harder to become timeless.
The real problem (well, it's hardly a problem, but we'll call it that for this argument) is the continual progression of gaming as a platform. Gaming is still young, and with the continued rapid advancement in pretty much every related area, we're constantly finding new ways to perfect the interactive.
The upshot is that games that were previously considered revolutionary or amazing quickly look dated and clunky. A control system that's seen as adequate in one decade is reviled in the next (see 90s PC gaming). Camera controls are perfected, movement becomes more fluid, new ways of perfecting development and presentation are developed. A technological advance that blows people away at release becomes unimpressive and even expected five years later. This is why so many people now playing Half Life 2 don't quite get it; for the time, it really was something special, but now it's no more than we expect from a game, in terms of immersion and graphical quality. (That said, it personally still holds my interest far better than many FPS games with similar premises but inferior execution.)
That's not to say that games can't become timeless, or that older games can't be enjoyed. I still play Future Shock, and I still consider it the greatest video game ever made. I can still play through Deus Ex and love the cyberpunk story. While I will freely admit that the first one is buggy and primitive, and the second has the clunkiest FPS combat I've ever played, along with some of the shittiest voice acting, they still engage with me because of their setting, atmosphere, plotline and sheer heart.
So no, don't feel bad if you don't appreciate a "classic" game (unless that game is Okami, you monster) - aside from personal taste or anything else, the industry might simply have done exactly what it should; use the game as a spring-board to go and make something better.
Though while we're in a thread where I can basically pick a fight, let's pick a game that I think is overrated in any generation: Ico.
Oh yeah, I went there! This game didn't just aggravate me on its HD re-release; I hated it on PS2 too! The art direction might be above-par, and the sound design is simply excellent, but the controls are atrocious, the camera is worse, and Yorda is in desperate need of a few solid kicks to the cranium. As an art piece it might succeed, but as a game it's frustrating and broken. The movement controls are stiff and cumbersome, and the combat controls are worse. Also, combining camera-relative controls with an auto-tracking camera is just asking for trouble. Put it this way - if I say the following...
One gigantic escort quest where you shepherd an incredibly thick utterly useless person with poor AI through a dangerous world via the medium of horrible controls, and if you step more than ten feet away from her at any given moment you will both almost certainly immediately die.
...you're going to think I'm talking about Amy. Yes, I just compared Ico to Amy. Why is one lauded when the other is rightly savaged for its gameplay?
I'd go into more detail on why I really don't like the game, but it would turn into an even longer rant. I'll leave it by saying two things:
1) The post-credits ending, which I won't spoil, can drown in an infinite sea of fire ants.
2) The HD collection can join it. When Sucker Punch update a game in HD, they improve the camera and controls while they're at it. Team Ico gleefully preserved the more horrible aspects of their design for future generations. If games don't age so well, why not take the opportunity to improve on the bits that have dated the worst?