I have to agree with you there, Matt. There was a certain charm to the old school games where realism didn't matter. The NBA Live series is an example of that. When NBA Live 95 was first released people had a lot of fun with it. By today's standards it's primitive and the gameplay certainly isn't realistic, but at the time it was entertaining. People found ways of making it realistic as such matters became more important, but for the most part we simply enjoyed taking control of our favourite NBA team.
One of my all-time favourite games is
Pirates! Gold, which is actually a remake of
Pirates! a game released a few years earlier. The game allows you to adopt the life of a pirate captain, ignoring the fact that piracy on the high seas wasn't as glamarous as it's often made out to be; it's the traditional image of pirates rather than the accurate historical portrayal, though there are certainly historically accurate elements to the game. A highly entertaining mixture of strategy and action, it's actually be remade again for today's gamers and will be out later this year.
Throwing some other names out there...Doom I and II, the Commander Keen series, Street Rods I and II, Lemmings (and its sequels), the Monkey Island games (which are still going, of course) and other LucasArts games, Super Mario Bros, Leisure Suit Larry, the Donkey Kong Country series and even more recent games such as the two Nintendo 64 Zelda titles and many more. Some of these genres have certainly been phased out or exist in very different forms today.
Sometimes it's nice to get out these old games; after all, nostalgia can be a pretty cool thing.

They represent a time when games were simply made to be fun rather than realistic or visually stunning. Today's games are awesome, no question, but there are some old school games that are simply timeless. I think many of them were more challenging as often you couldn't save games in progress so you had to sit down for a while and play your best to finish it.
To be trite, these games had soul, an element that some (but certainly not all) of today's games seem to lack. Some of today's games seem sterile, flashy but lacking substance. As I said before, some gaming genres have become extinct or exist in very different forms.
Realism is nice, and I wouldn't want the NBA Live series to be arcade-ish or revert to NBA Live 95, but yes, there's certainly a charm to the old school games.