In 1999, after the Speccy Microdrives were a decade obsolete, IBM released their own Microdrives. Instead of tape drives, the IBM Microdrives were then-revolutionary 1" diameter hard drives crammed into a CompactFlash form factor. At a time when a large, expensive flash memory card might hold 128 megabytes, the initial Microdrives could hold 340 megabytes and had much faster read/write times, as well as a surprisingly good cost given the amount of storage. Now, Microdrives come in 1, 2, and 4 gigabyte capacities, at a somewhat-better price-per-megabyte cost than traditional flash memory CompactFlash cards.
This didn't come without tradeoffs, To start, Microdrives aren't quite as durable as flash memory, so they couldn't withstand really nasty shocks or temperature changes. (In practice, they are plenty durable, but keep in mind that working CF and SD cards have been recovered from collapsed buildings and tornado strikes.) Microdrives are CompactFlash Type II devices, so they're slightly larger than most CF cards, so some devices can't use them. Likewise, Microdrives take a bit more power than the CF standard allows, so they can be unreliable or just plain nonfunctional in some devices.
Microdrives were never particularly popular, as their low cost-per-megabyte could only do so much to reduce the initial sticker shock. (Even now 1 gigabyte Microdrives cost upwards of $100.) Nevertheless, they found a niche. Professional and prosumer photographers favored them for their ridiculously huge storage capacity, allowing them to take as many print-quality, high-resolution photographs as they'd like. PDA aficionados favored them because...well, PDAs don't come with hard drives, and Microdrives allowed for what felt like unlimited storage space for PDA users used to 64 megabytes of storage, tops.
"Microdrive" is a trademarked term, but occasionally you'll hear the word "microdrive" used to refer to the 1" hard drives used in both Microdrives and a number of small electronic devices, most notably the iPod Mini. Occasionally devices like these simply have Microdrives (with the CF interface and everything) inside the casing, which lead to photographers and PDA fans buying these devices and ripping them open for the Microdrives inside. (The Creative Labs Nomad MuVo2 and its 4 gigabyte Microdrive was the most infamous example of this; online retailers couldn't keep them in stock for people buying them to rip apart.)
Microdrives are practically obsolete, now, as flash memory costs have come down. Microdrives are now only marginally cheaper than CompactFlash cards of the same size. Moreover, Hitachi (who bought out IBM's disk drive business in December 2002, including the Microdrive brand) hasn't come out with 8 gigabyte Microdrives to go along with the 8 gigabyte CompactFlash cards SanDisk has rolled out.
Sources: The wikipedia article on Microdrives, Hitachi.com, SlickDeals.net