Games are worse in some ways, and better in others. There are games being made today that simply couldn't be made previously, or would have been (or were) much weaker in the past.
The problem is a fewfold. First, there is a tendency to insert excessive narration into every game. Old games often lacked much in the way of narration, and that was a good thing. Sonic Colors doesn't really NEED a story beyond the levels. Why bother putting one in?
Secondly, there's a tendency towards making games easier to play. This is not a bad thing, but the badness enters when you lack anything to sink your teeth into. Oftentimes appropriate difficulty levels have to be unlocked, but because the game is so easy there's no point in sinking in the time to get the challenge you want. In many cases, AI is quite bad; while AI has always been terrible, a lot of enemies now have bad AI instead of actual patterns which were more fun to play against and weren't any less difficult to defeat, and in many cases allowed for more difficult situations because of multiple enemies in the same area adding up in more interesting ways.
The genre in which this has its greatest negative impact, however, is platforming. Making a more difficult platforming game requires you to make new level layouts, so difficulty levels are without meaning most of the time; you have whatever level there is, and that level is now lower than it once was. Moreover, a lot of these levels are less complicated and more samey than they once were, and in many cases, especially 3D platformers, much more linear. Super Mario 64 was cool precisely because the world you were in was open; in Super Mario Galaxy, they put you on rails and there were no really interesting shortcuts to take or decisions to make. You just felt like you were going the way you have to go... because you were.
Platformers are the genre which was hardest hit by the decrease in difficulty, and it had a devastating impact on them. How many good platforming games came out between Mario 64 and New Super Mario Bros? The answer is a depressingly small number. Only in relatively recent times have good platformers begun to appear again - and many of the good ones are 2D. Indeed, the platformer market is so bad that people saw Braid as a good game, a charge that never would have been leveled at it in the 90s.
Thirdly, lots of games have a lot of unnecessary side content or collectables. This is bad. Don't throw in random crap for no good reason; everything in a game should have a purpose in being there, or not be there at all. RPGs are particularly bad offenders at this, with sidequests galore, but all genres of game have been affected by this. The games are often unfocused as a result of adding in too much to do and not focusing enough on what you SHOULD be doing. This problem barely existed in the early 90s, but as people got more and more memory to play with, they began to add more and more extraneous content, not realizing that by doing so they were weakening their game, not strenghtening it by adding the new content.
Finally, a lot of games lack an actual reason for existing beyond profit motive. The issue here is that you have games which come out but don't really try to give you any sort of particular experience, but which simply exist. A lot of FPSs fall into this category, but there are plenty of other examples as well of "empty" games - games that you can play but feel hollow. Super Mario Galaxy, Killing Floor, Borderlands - these games have been lauded, but there is nothing substantive to them. And many games are much worse than these in terms of having actual substance to them.
The ways that games have gotten better, beyond graphics, is more consistent controls across games and indeed genres, the ability to stretch further, more exploration of fields that were previously very difficult to explore (FPSs and other games like it do benefit greatly from improved graphics, and it allows you to set games in environments which simply didn't exist before because they looked too crappy to immerse you in them), and a general increase in content.
But a game is both an investment in time and money, and if I don't have fun fast and keep having fun, I'm likely to drop the game.
