I used to think a lot like you. Then I started thinking some more, and went back to the older days to find that games really weren't that much better back then.
-Graphics vs. Gameplay vs. Plot; yes, gameplay/plot are important factors in a game.
But honestly, I won't buy a new-gen game for full retail price if I think it looks bad.
My standards aren't very high, but I won't accept 64-bit graphics on my HD consoles, a good experience excuses a lot, but not everything. Might be hypocrisy, but that's just the way it works for a lot of people.
As for plot vs. gameplay, I think others have said it well enough. A good plot does not excuse bad gameplay. I like games with a strong -and preferably surprising and original- plot, but if they're no fun to play, I'll go read a book.
-Storyline; These are (generally) much better now than they were in the SNES days. Sure FFVI has a better storyline than Halo, but that can be expected from comparing a story-based genre to an action-based genre.
Modern-day shooters have more story and gameplay elements than they did during the SNES days. Even if -Like me- you don't like the direction they've taken gameplay-wise, it's hardly fair to say the games have gotten worse than 15 years ago.
One hero to save the universe isn't really something new. Mario got killed plenty of times before defeating Bowser, Robotnik probably won the fight more often than Sonic did, and the Game Over screen in any classic Final Fantasy has been seen a lot more than the end credits.
-I'll skip the FFVII rant. I'm not a big fan of the game myself, but that's all up to personal preference really.
-Old vs. New; Personally, I don't think games have really gotten that much worse. We just tend to remember/replay only the good games from our childhood, turning them into a more glorious memory than they really deserve.
Comparing the average games from those days to the average games of today will probably show that games have gotten a lot better. Of course there are some gems from back then that are hard to beat in whatever they were best at, but that doesn't mean everything was better.
Apart from that, people grow older, and after playing a lot more games we've become a lot more demanding than we once were. When you were young, you probably liked children's books a lot more than you do now. Doesn't mean modern books suck, it means you have different needs and demands than you did 15 years ago.