As a long time lover of all things animated, I'd like to jump into this.
I think it's a matter of perspective as to whether cartoons back in the 80s or cartoons of today are better. If you really go back and watch a majority of 80s cartoons, almost all of them are GOD AWFUL. If you were a fan of Voltron as a kid, I dare you to watch it now. I bought some of the DVD boxsets, and I couldn't get through box set 2 before I sold them all. They were that bad. I could even tell all the areas that were edited from the original Japanese show (without ever seeing the original Japanese show).
Unless it was made by Disney, most cartoons from the 80s had incredibly low budgets and looked and sounded horrible. The writing was bad and everything in a lot of them felt uninspired.
Don't get me wrong, there were a bunch of classics from the 80s, but I think they're just that. Classics. The reason we love them so much is because they were from a majority of OUR childhoods. Today's cartoons don't represent a part of our life, mostly because we won't let them, due to us clinging to the cartoons of our childhood.
Once again, don't get me wrong, there are A TON of horrible cartoons of today. But there are a lot of really good ones, and I'm not just talking about the more adult ones like Family Guy, The Simpsons, South Park and anything off of Adult Swim. (my personal favorites list is below)
I'm sure if we tried to get some kids today to watch the cartoons we loved as kids, they'd probably not want to watch that much. Like I said, it's all about perspective.
I also think part of the problem is that there are so many more outlets for cartoons nowadays. When we were kids, we only had four or five channels that showed cartoons every Saturday from 8am-12pm and maybe one of those channels showed cartoons when you got home from school. Nowadays, there are countless channels with animated programming, some of them are shown 24/7. Cartoons just don't seem as important anymore now that they are more widespread.
And, of course, there is the age issue. As you grow older, animated shows (which are wrongfully labled as "kids programming") just aren't socially considered programming older people should watch. So you probably feel justified in both hating today's cartoons and being justified in liking the older cartoons, because you watched them when you were the socially approved age of watching those programs.
There are a lot of stinkers in the animated world today (that list is also below), but I think to just pass off animated shows just because they are the "cartoons of today", isn't a fair judgment to pass.
Some of the best cartoons of the past decade or so include:
The various Batman and DC Comics Series (Justice League)
Jackie Chan Adventures
Foster's Home For Imaginary Friends
Misadventures Of Flap Jack (my current favorite)
The Wild Thornberries
K.I.D.S. Next Door
Courage The Cowardly Dog
Billy & Mandy
Avatar (I haven't seen a lot of this, but what I've seen is pretty good)
And some of the worst:
Total Drama Island / Action