Developer: Sega
Sega Genesis 32X Specifications:

CPU - Two Hitachi 32-bit RISC processors running at 23MHz/40 MIPS
Co-Processing -
Genesis 68000, Z80, VDP and 32X VDP
High-speed RISC processors and dual frame buffers rendering up to 50,000 polygons per second for arcade-quality texture mapping, hardware scaling and rotation
Colors -
32,768 simultaneous colors
Memory -
4Mbit RAM on top of the Genesis and Sega CD Memory
Video -
Overlays an additional plane of graphics over the Genesis video
Audio -
Delivers stereo quality audio with programmable sample rates; audio mixing with Genesis sound
Official Ad: Yes - Ad 1, Ad 2 , Ad 3, Ad 4
Finally got one that worked for: Free! Complete, in box, with manual and all cords!

My history with the 32X:

32X #1: Bought it at Toy's R Us, new, for $19.99: It worked with *some* 32X games, and *some* Genesis games wouldn't play through it(one of these being Light Crusader). After fighting it constantly, through freeze-ups and it's refusal to even start some games, I gave it to a friend. This was before I knew about the simple wire fix.

32X #2: Bought it at a pawn shop: It never worked, I took it back.

32X #3: A friend of mine's brother knew a guy who had one, didn't want it and persuaded him to GIVE it to me! Had some trouble at first with this one, but after I opened it up, plugged in a seriously loose wire and messed with the conversion cable a little I got it working! Haven't had any problems since(crossing fingers).

Ah, the 32X, the beginning of the downfall of Sega. Consumers, apparently, just weren't ready to dish out the hefty starting price of $149 so late in the Genesis' life span. That's a real shame too, as the 32X had so much untapped potential and a solid library of suped-up games. Though the general gaming public mocks and hates it, I find this to be one of the greatest systems out there, and a more than worthy addition to the already spectacular Genesis/Sega CD combo.

Graphics - More than anything else, the 32X's new color palette and color output are the system's shining achievement. Almost every game out there made a good use of it, and titles like Tempo and Kolibri went so far as to blatantly flaunt it. The other main strength of the 32X comes from its ability to, now, adequately handle massive amounts of polygons through its set hardware. Games like Shadow Squadron and Metal Head show off some impressive numbers and nice scenes with their polygon based worlds.
Sound - I have no idea what the 32X does for the sound. I mean, yes, there is a lot of speech in some 32X games, and it does sound a bit better than regular carts using just the Genesis' sound chip, but it's nothing like what the specs have it hyped to be.
Library - With only a meager 39 games released, 3 of which never made it domestically, the library is seriously lacking in sheer quantity. Now, as few games as there were, the number of quality titles for the system is extremely high. With games like Knuckles Chaotix, Tempo, Shadow Squadron, the best console(16-bit) version of Mortal Kombat 2, etc. it's easy to see how you could very quickly find yourself owning almost every game released.
Installation - Hooking it up to the Genesis, for the first time, can be a real pain. You don't know what you're doing, there are so many wires and you just want the damn thing to work! After putting it on the Genesis for the first time though, you begin to see how easy it really was. Now, taking it off to maintenance the thing, that's a whole other story...

Gaming Value - Very high. Though I can't say I would have paid $149 for it, had I of had the money and/or chance to pick it up when they dropped it to $79, I would have done so. Nowadays, the systems are $30 max, a small price to pay for such a great add-on.

Tips for better gaming experiences:
32X not working? Freezing up in the middle of a game? Some games make it to the title screen, then give you a brown screen filled with code errors? Well, my friend, sounds like you have 32X internal wiring issues(don't worry, it's not your fault, *every*{and I mean *EVERY*} 32X owner goes through this). From what I've seen and read, the problem lies in two white wires located directly below the cartridge slot, under the casing. These have a tendency to come loose from time to time(some say it's the heat that will do it), and when they do, you WILL see things going wrong. Fear not, it's a simple process to accomplish. The best guide I can provide to you would be from the great guys at Sonic Cult: Their 32X Repair Guide is the best I've ever seen and with the pictures provided, it makes for an extremely helpful walkthrough on getting the old 32X working again for you.

CDX, X'eye?
Yes indeed, even though Sega has many contradicting reports on the CDX and 32X's compatibility, it does indeed work. For a great walkthrough on getting your 32X up and running with you hip, little CDX, be sure to check out x56h34's Video Game School walkthrough. He has also completed a guide on how to get the JVC X'eye to work with your 32X. Good stuff!!! Also, for a great walkthrough on basic 32X installation, on a Genesis 1 or 2 unit, check out Abe Mnemonic's 32X Install Guide.

My rating: 90(out of 100) - Dirt cheap nowadays, excellent handful of games and sits quietly, as it lets you play Genesis and 32X games through it. An ultra-powered add-on that you *need* to own!

JD's angry opinion:
Jeez does this system suck...especially compared to the next step up, Saturn. Why anyone would waste time with the hassle of not only finding one, but constantly repairing the damn thing is beyond me. I'm sorry, three or four decent games are not enough for the trouble. Reow!

Interesting Tidbits:
The 32X will allow you to play imports, that have no regional lockout, due to its larger cart slot. Also, older EA and Accolade games(like Double Dragon) that would not play on your model 1 Genesis will now play through the 32X.

32X Ecco?

Yes indeed, a new Ecco game was said to be in the works while Sega was showing off the 32X's hardware in the development phase. They released on demo, an impressive bit of footage showing off the 32X's video clarity. To check it out, click here. Please note that my gif does not accurately portray the video footage's framerate(it's much, *much* smoother when you see it running via Gens).

Serious thanks go out to Daniel Crocker at Games Department for his help in converting the awesome 32X Demo Tape from WMV to MPEG, so I could then encode it to Divx for *all* platforms to view.
Untapped Potential(X 32):
In a stunning showing of power, Zyrinx(the developers behind such titles as Sub-Terannia, Scorcher, Zero Tolerance, Red Zone and other games that pushed the limits of the hardware they were working on) stunned everyone with an amazing 32X demo tape. The footage shows off some of the 32X's abilities, from flat shaded polygons, to texture mapping and even gouraud shading. It has to be seen to be here and prepare to be amazed!

Immediate Streaming - YouTube
Note: You'll need the most recent Divx codec to watch this video.