What they were: A form of removable storage, in 3.5-, 5.25-, and 8-inch variants, that started in the 1970s as a high-end alternative to saving programs on audio cassettes, then segued into serving as a handy complement to hard drives.
What happened: Until the mid-1990s, floppies remained essential. But then the Internet came along and provided folks with file downloads and attachments--faster ways to accomplish tasks that had long been the floppy disk's domain, without floppies' 1.44MB capacity limitation. (Higher-capacity floppies arrived at about the same time, but never caught on.) Much higher-capacity storage media like Zip disks and recordable DVDs nudged floppies further towards irrelevancy. And USB drives--which provide a gigabyte or more of storage for less than what I paid for one 72KB floppy in the 1970s--finished the job.
Current whereabouts: Floppy drives are no longer standard equipment, but they certainly haven't vanished--in fact, you may have a computer or two around the house that sports one. New 3.5-inch drives and media remain readily available, and you might be able to find 5.25-inch ones if you hunt a bit. (8-inch floppies I can't help you with.) Which leaves only one question: Under what circumstances would you opt for floppies over something like a $10 (or so) 4GB USB drive that holds 2750 times as much data?
What they were: Iomega's extremely useful, cleverly marketed high-capacity removable disks--introduced back in 1994, when 100MB qualified as high capacity. They were never as pervasive as floppies, but they must be the most popular, most-loved proprietary disk format of all time.
What happened: The same things that happened to floppy disks, only more slowly--and complicated by the malfunction ominously known as the click of death. When cheap CD burners made it easy to store 650MB on a low-cost disc that worked in nearly any computer, Zip started to look less capacious and cost-efficient. And then USB drives--which offered more storage than Zip and required no drive at all--came out. Along the way, Iomega launched new disk formats such as Jaz, PocketZip, and Rev, but they failed to recapture the Zip magic.
Current whereabouts: Iomega seems to be doing fine as a manufacturer of storage products of all sorts. It still sells 250MB and 750MB Zip drives, along with Zip media going all the way back to the original 100MB disks. I confess that I never owned a Zip drive myself--but I'll still feel a twinge of sadness when they finally go away.
What it was: The 8-bit microprocessor, dating to 1976, that powered an array of early personal computers, including the Radio Shack TRS-80, the Osborne 1, the KayPro II, the Sinclair ZX80, the Exidy Sorcerer, and many others. It was also inside Pac-Man arcade games and ColecoVision game consoles.
What happened: Progress! Among the notable things about 1981's original IBM PC was its use of a powerful 16-bit CPU, the 8088. In time, 16-bit processors gave way to 32-bit ones, which have been superseded by 64-bit models like Intel's Core 2 Duo and AMD's Phenom.
Current whereabouts: Everywhere--but invisibly so. It's been more than a quarter-century since the chip's time as a personal-computer CPU ended, but it never stopped finding useful life in industrial equipment, office devices, consumer electronics, and musical instruments. Zilog, the Z80's inventor, still makes 'em. Anyone want to wager on whether the Core 2 Duo will still be around in 2042?