The Sega 32X was the final add-on for the Sega Genesis and was developed under the codename Project Mars. The Sega CD was not as successful as Sega hoped it would be in terms of offering higher quality gameplay that wasn't available on their competitors system. The concept behind the 32X was to upgrade the Genesis to play 32bit games which would be a huge increase over what was possible on the SNES. While the Sega Saturn was already under development the 32X was conceived as a stop gap in order to help the Genesis continue to thrive while the Saturn gained momentum in the market. The 32X was released in North America in November 1994 at $159 along with six launch titles: Doom, Star Wars Arcade, After Burner Complete, Super Motocross, Virtua Racing Deluxe, and Fahrenheit CD. In both Europe and North America millions of consoles were requested by retailers, but Sega shipped much less (600,000 in North America), which led to supply shortages.
Like the Sega CD the 32X required a Genesis to attach to, and also required it's own AC adapter to provide power to the system. A third cable connected the 32X to the genesis (and CD if available). This cable passed along the second layer of the video to the system, surprisingly 32X games play without the video cable, but only background images are shown on screen without the sprites. Also several 32X titles were released on CD's and required both the Sega CD and the 32X to be attached in order to play. Only 5 Sega CD/32X titles were released, but they showcased what the combination was able to pull off, the most notable being Night Trap which boosted 5000x the amount of colors on screen using the 32X compared to the original Sega CD version. As most Sega CD games were known for their terrible quality FMV sequences this was quite an improvement.
Although not specified the 32X is compatible with the portable CDX system, and by removing the plastic bottom of the 32X it can fit within the JVX X'Eye unit as well. While both the CDX and JVC X'Eye can then play 32X games, the 32X blocks the disc drive from opening so it must be removed in order to play any CD games.
Also unlike the Sega CD the 32X did not require different variations depending on which Genesis the player owned. The 32X fit within both the original Genesis and the Genesis 2, an included pair or metal clips was required for attachment to the Genesis 2 however. The 32X also acted as a pass-through so that it did not need to be removed in order for the user to play original Genesis games, however the Master System Power Base Converter could not be used with the 32X.
Titles in other regions were region protected preventing importing. However, probably in an attempt to release as many games in North America as possible in order to build awareness, all but one Japanese title was released in North America for the 32X.
In mid 1995, the 32X's popularity began to decline as it was abandoned by developers. Despite being touted a true next gen 32bit console, developers felt they had accomplished close to the threshold of what the system would allow technically. This was not apparent to consumers as most games seems to only include minor features and technical updates over Sega Genesis games. Despite Sega's promise to support the 32X after the release of the Saturn, the developers shifted focus to that console and 32X development and promotion stopped. In October 1995, Sega's CEO, Hayao Nakayama, ordered that the 32X production to be canceled in order to focus on the Saturn system. This included the prototype Genesis/32X hybrid, the Sega Neptune. Many retailers offered their very large amount of left over stock at liquidation prices, and despite the prices, the found the console still difficult to clear out. The final several 32X games released in 1996 we released in such low quantities that they have become expensive collector items.
Getting a Sega 32X
Aside from the 32X add-on there is no other official way to play 32X games. None of the cloned Sega Consoles support them, nor are they available on any download service. While the systems are not that easy to come by now, they are also not that expensive. You should be able to find the add-on itself (sometimes even complete with box) for less than $100.