Sega CDX

One of Sega's many "doomed" systems released between the slow death of the Genesis and the release of the Saturn.

It was a Sega CD the size of a doubly-thick cd player.

Cost around $300 on release, but worth it for its portability and enormous game library. Less worth it if you already own a Genesis, and worthless if you already own a Sega CD as well.
Who would buy this except someone who already owns and loves Genesis games? And who would re-purchase a console they already own? This system was really just an eccentricity, and was released in only in small quantities.

A neat idea, but a flawed one.
It was, in fact, a two in one system, Sega Genesis and Sega CD as a single convenient unit. I think it was meant as an alternative to the modular design of the whole Genesis suite, i.e. it's a 16-bit cartridge system, add another unit and it's CD-based, add another and it's 32-bit. But what if someone just wants Sega CD games? They don't want to buy an extraneous console. CDX was the answer.
Of course, you still had an overpriced system. And the 32X wasn't included. And there simply wasn't enough consumer interest and hence, not a large production. As an attempt to revitalize the Genesis market, it was a flop.
It is, however, next on my list for my console collection.

The Sega CDX doubled as a line or battery-powered portable CD player (a.k.a. Walkman®). (Thanks to gwm for pointing out that games could not be played on battery power.) Apparently the play time on a set of batteries was quite long compared to other portable CD players from that era.

Sega CDX FAQ: http://faqs.ign.com/articles/428/428996p1.html

It should also be noted that Sega says that the 32X is incompatible with the CDX. This is because Sega was either unable or uninterested to get FCC approval for the combined unit.

However, in practice the 32X will connect to the unit and play just fine. Of course, if plugging the 32X into the unit causes an explosion, meltdown, or mutation then Sega isn't responsible.