Gotterdammerung said:
Old Game: Long levels, few checkpoints, limited lives.
New Game: long levels, many checkpoints, unlimited lives.
First off, the bolded aspects are what is called "Fake Difficulty" [http://tvtropes.org/pmwiki/pmwiki.php/Main/FakeDifficulty]. More distance between checkpoints and a limited number of attempts does not mean the gameplay itself is innately more difficult to execute, it just means that you are more penalized for screwing up. If you die, you go back further; if you die too often, you have to restart. These aspects are probably just a remnant from when games were only coin-op arcade machines; it made sense back then because you had to pay for each number of attempts, it created more profits for the owner of the machine.
With home consoles (or personal PCs) being the dominant format today, these limits make very little sense because the developper isn't making any money off the game after the initial sale. In fact, it's in their best interest for the player to complete the game so that they're able to move onto the developpers next product. As such, most games are simply more fair in their challenges; this could also be the reason games have been getting a bit shorter in the last decade or so. Fortunately, game developpers make the effort for generally high-quality experiences that allows for a great deal of replayability.
There still is one genre of games which still favours a high degree of fake difficulty (for those who enjoy that sort of thing), and it would be the MMORPG. While WoW's popularity (and accessibility) has killed some forms of fake difficulty (i.e.: experience loss upon death), it retains at least one type in the form of random drops; this trick serves no purpose other than to make players re-do the same content and keep playing the game... and paying their subscription to do so.
Another thing which makes games feel easier these days is a gentler difficulty curve, good tutorials are more common. The player isn't stonewalled with a challenge they have to look at outside the game to gain the insight needed to overcome it, but the games make the effort to incorporate teaching the player how to play... as they play the game. Of course, we've seen a few examples where it's been taken too far (usually when the game reminds a bit too often how to do basic things) but the general trend has been towards more accessibility. A good example of this is seen in the
Super Mario series (the platforming games in particular, not the spin-offs), all of which are very accessible (and easy) at the start but still present a great deal of challenge towards their conclusion. You can almost say that each game is mostly made up of tutorials, teaching you how to use each element of the gameplay in a different way that you'll be using later on in the game.
Nevertheless, with the general market of games these days not being of the pay-to-play variety, it makes no sense for developpers to include large amounts of fake difficulty. Fair games sell better (more accessible), and the developpers gain no profits from games which artificially increase their length with unfair challenges. The net effect is that games FEEL easier, but it's just because they aren't cheating so much anymore and make the effort to have good tutorials.