When you combine a ball of fur with eyes, a large nose, and legs with a short temper hopping all over the place with a bunch of weird-looking creatures to chase him around a pyramid of color-changing blocks, in a nutshell you have Q*bert. Hours of cube-hopping fun and frustration for everyone are to be had with this arcade classic. In addition to two sequels (one of which was extremely rare, the other nonexistent, more on these later,) numerous product tie-ins and even a Saturday-morning cartoon, Q*bert was actually quite popular at the time.
Basically, as was mentioned above, the idea of Q*bert is to hop around the pyramid of colored blocks, and change all of the tops of the blocks to a target color, which is shown above. Of course, given that video games really aren't supposed to be easy (with the possible exception of Leprechaun) there are quite a few different creatures on the pyramid bent on your untimely demise (or at least making Q*bert mad.) In addition, there is also the hazard of accidentally jumping off the pyramid with a loud thunk (in the actual arcade machine, a pinball knocker was used to make this knocking sound), Each time this is completed, the task becomes harder with blocks that need to be changed twice, blocks that change back if jumped on again, and even (you guessed it) blocks that need to be jumped on twice, but change back if you jump on them again! All this, and when you clear one pyramid of the things, another one awaits you, with more expletive-inducing enemies and perils.
This is Q*Bert, the protagonist of the game. Q*Bert has such amazing powers as hopping around with ease, changing colors of blocks on the pyramids, swearing up a storm whenever he gets mad, and..... Uh..... Well, lets move on.
Red Balls do nothing more than start at the top of the pyramid and fall down one step at a time. Usually easy to avoid, but they can get in the way pretty fast if you're not careful.
The Purple Ball begins by starting at the top and falling down the pyramid one step at a time, but instead of just unceremoniously falling off when the bottom is reached, purple ball turns into...
Coily. This purple snake will chase you all around the pyramid, and has this strange tendency not to be a very pleasant fellow to run into for some straneg reason. Fortunately it is possible to lure Coily off of the pyramid using...
 
...the flying discs at the sides of the pyramid. These discs will whisk Q*bert back to the top of the pyramid with the greatest of ease, while Coily, having the brains of a reptile (or a few lines of assembly code), will jump off the pyramid right behind you, falling to it's doom, only to be replaced by another purple ball coming down just seconds later.

Wrongway and his brother Ugg both go up the pyramid, hopping on the sides of the pyramids. They also have the ability to chase Q*bert, but can only go to the side and up. In some rounds, these replace the red balls falling down the pyramid.
Unlike many of the other enemies, Slick cannot hurt you, but can also be rather annoying. When he hops down the pyramid, all of the blocks he jumps on will revert back to their previous color. If you do manage to stop Slick first, however, you will gain bonus points.
Finally, there's the green ball, which also falls down the pyramid, but not only do you get bonus points for collecting these, but picking one up will freeze all of the enemies on screen for a few seconds. Green balls can come in handy when a lot is going on at once.
Q*Bert's Qubes is the rare sequel to the original Q*Bert, and other than the basic themes, bears little or no resemblance to it's progenitor in gameplay. The goal of Q*Bert's Qubes is to make lines across the board, Tic-Tac-Toe style. When Q*Bert hops on a cube, instead of changing the color, the cube rotates in the direction of the jump, and when the target colors for the sides of the cube are reached, that cube is cleared, and can no longer be changed. The enemies are somewhat changed in this game, but in most cases act exactly the same as the enemies in the predecessor. The spinning discs are gone, but the possibility of falling off the edge isn't. IMHO, I actually like this one quite a bit more than I like the original Q*Bert, even though for obvious reasons I never played it in the arcade.
Another one which it's likely that nobody out there has seen before now is what's euphemistically known as "Faster, Harder, More Challenging Q*Bert," of which the only arcade exposure was brief playtesting in 1983, after which production was nixed. As the name implies, this one plays quite similarly to the original Q*Bert (in fact, it IS the same gameplay as the former) and is in fact faster, harder, and more challenging. For example, the spinning discs in FHMC Q*Bert actually move on you if you aren't careful, andyou must time the jump carefully to make sure you aren't going to fall when the disc moves. The levels get harder much faster than in the original. Although as of yet I haven't been able to get past the fourth screen on the first level, eventually you reach bonus stages, where the idea is to catch as many slicks, sams and green balls as possible, then you run into Q*Bert's worst nightmare: Q*Bertha. As of yet, I don't have pictures as I haven't reached that far. (More on this a little later.)
The joystick in Q-Bert cabinets was mounted at a 45-degree angle, in order to accomodate the control of the game more effectively. Also, as was mentioned before, there was a standard pinball knocker built into the cabinet, in order to add an extra "thud" sound when Q*bert fell off the pyramid. This was controlled by a DIP switch, and if you look in MAME, this setting is available, although at the present time, there is no effect from this for obvious reasons.