My first experience with video games was back in the early-eighties with the Intellivision. While the games such as Astrosmash, Space Battle, and Lock 'n Chase weren't very pretty to look at, they still were fun and had lasting appeal. I sometimes still have a desire to hook up the old Intellivision system from time to time.
However, it wasn't truly until around 1988 when I started really getting into games. For Christmas that year my brother and I received a NES system. Me, my brother, and my dad had gone to a local arcade and played Super Mario Bros., and, at that age, I simply thought that game was amazing (and, in fact, at that point in history, it was amazing). Needless to say that I very much enjoyed having that particular game at home, as well as Duck Hunt (included, of course, with Super Mario Bros.) and Excitebike.
Currently, I have around 70 NES games, many of which I have picked up within the last 10 years or so. Many older games have a great lasting appeal to me. At first, I think that some of this may have to do with nostalgia. It's easy to think that something is good simply because you did it or had it as a kid. But the only problem in my circumstance is that many of the games I have now I never played when I was a kid. I have come to a few conclusions as to why I enjoy these older games so much.
First of all, I believe many old games were meant to be "challenging," while many newer games are meant to be "beaten." By this I mean that it is challenging to play many older games, but many newer games offer you various difficulties of play or are made to be beat fairly easily. I can't tell you how many times I played a game like Double Dragon and failed to beat the game. Now, this isn't to say that no newer games are difficult. Don't try to tell that to anyone who's played Ikaruga or Contra: Shattered Soldier. But other games, especially most RPGs, are made in a way that is not difficult for people to beat. For example, a game such as the first Final Fantasy, could be much more difficult at times than the newer Final Fantasy games. Of course, some of this (from an RPG standpoint) has to do with less "leveling up" and more of an involved storyline, but I digress.
Secondly, the older games are much more simplistic than newer ones. The simplicity can have its drawbacks, but I think that such games can have a greater appeal over time because of that simplicity. For example, while the current line of Madden football games have tons and tons of customization, and simulate a real football game pretty well, you have to spend a considerable amount of time learning the game. A game such as Tecmo Bowl, however, is easy to pick up in comparison. Of course, sometimes older games are more difficult to completely master (as related to my first point, above), but the point is that many older games are easier to learn. You usually don't have to put as much of an effort in learning them like many newer games.
Lastly, some of the most storied franchises today first came to be on older gaming consoles. Some of these franchises include Mario, Zelda, and Sonic. While there have been vast improvements every time a new version of these games comes out, they still all originated from an older game or games. Many things from the newer games are borrowed from older ones, such as music, gameplay, items, etc. While this is not necessarily a great reason in itself as to why older games are more appealing, it does show that there are many others who also realize how great some of these games are. Just how many recent games would you think would be considered just as influential 10 years down the road? Many games that people would say, such as The Legend of Zelda: The Ocarina of Time and Grand Theft Auto III, while being revolutionary in themselves, still owe their existence to older games. The appeal usually originates in the predecessors.
My point in all of this is not to say that older games are necessarily better by any means. Quite the contrary, I enjoy many newer games. It's just over time I would still probably enjoy playing the first Metroid over Metroid Prime.