NetHack

Back in 1980, when all anyone could get computer-wise was a little system called Unix, computer games still played a fairly prominent role (Factoid: Unix, arguably the first OS, was originally developed for the sole purpose of playing a video game. Suck on that, Jack Thompson. Tastes like... history). They were understandably simple of course, often being simply text adventures. ASCII characters were not, however, only used for writing text. The greatest example of this was probably Rogue, an adventure game where you were a little "@" symbol running around, killing "Z" zombies and other baddies (one of my favorites is the "grid bug", represented by an "x" and notable for being killable in about one hit. To be killed by a grid bug is the lowest disgrace imaginable. I have been killed by grid bugs numerous times). So to answer your question, yes. Yes you can totally still play Rogue today, but why would you want to? There's an entire genre of games called rogue-likes, and the fan base they have developed is nothing short of astounding (the über-popular Diablo series are all rogue-likes). While Rogue was a somewhat boring and simple adventure game, one of its descendants, NetHack, is almost universally recognized as one of the greatest games ever made. Really. No sound, no cutscenes, you don't even need a color screen, but it's still that good.

NetHack was first created in 1987 and while it was a spin-off of Rogue at first, it quickly took the gaming world by storm and became a revolution all its own. First off, there are the numerous versions of the game to be had. You can get it with graphics that make a game look like some cheap Zelda knock-off, while purists will insist upon playing it in Terminal with the original ASCII characters and admittedly horrible controls (Left=H; Right=L; Up=K; Down=J. Yeah, go ahead and look at your keyboard. You get used to it, but just barely). The other drawing point is the gameplay. Game designers wish they had this much content in a game. Among the more interesting things of note, there are gods to be prayed to (and to be angered. They can mess your world up but good), curses, magic, djinn (genies who allow you to essentially commit genocide and choose one species to kill in its entirety), shopkeepers you can buy or steal from (don't bother, most are wicked accurate with a wand of lightning), and an animal sidekick to follow you around. I like the kitten even though it's freaking worthless.

You can find the homepage here, and I would totally advise putting in the effort to install the original ASCII version. Everything pertinent to the game (full item lists you'll need in the unlikely event that you ever make it off the first level, whether or not you can cook and eat the corpse of a goblin king [you can't]) can be found on its unofficial wiki, WikiHack.

P.S.: The game has been ported to some unassuming devices, including the Nintendo DS, the iPhone and numerous cell-phones. If I had that, I would totally use my phone for more than keeping technophobic ghosts at bay (It's getting to be kind of a problem).