There were a number of different models of the Commodore 64 throughout its long lifespan. From the introduction of the famous "breadbox" model in 1982 (at a list price of $600) to the models demise in the early 1990s Commodore tried out various configurations and case designs in an effort to keep the 64 both relevant and selling. This is a rundown of the most famous of these variant models.
The first to be announced was the SX-64. This was a transportable or "luggable" computer, similar in layout to the Kaypro II or Osborne computers that were popular at the time. Kaypro and Osborne were just the most famous manufacturers, this horizontal oriented case design with the floppy disk drives to the right of a 9" CRT monitor was a standard for the form factor. By contemporary standards it is a huge, heavy, clumsy machine - not something you would ever want to carry around with you. But by the standards of 1983 these computers were something close to a miracle - an entire computer system in one case, with a handle! When the decade before the smallest computers were the size of a desk, not a desktop, the size and weight were overlooked. The SX-64 went the Osborne and Kaypro one better in supporting color - it was the first portable color computer. Unlike a laptop or notebook computer, it could not run on batteries; it needed to be plugged into an outlet to run, although car lighter socket adaptors were available. The SX-64 was not a big success as it appealed mostly to businessmen who were more interested in CP/M and MS-DOS transportables than in the 64.
Another interesting variation on the C-64 theme was the Educator 64. This was introduced as a follow on to Commodore's PET series, which had attained some success in education. Schools that wanted to upgrade to a new Commodore model, rather than switch to the Apple II, which was quickly becoming the standard, were told about the Educator 64 - a refurbished C64 motherboard inside a PET-like case, with a BASIC 2.0 cheat sheet printed on the front. The monitor of the Educator 64 was "greenscale" displaying color as different intensities of green. The Educator 64 did not gain much success since most schools did elect to buy Apple equipment.
A third variation came a little later, after the 64 was already the best selling home computer in the world. The 64c came out after the 64s supposed successor, the Commodore 128 was introduced. The 64c looked like the 128, clad in the same off-white angular case that echoed the design trends of the time. Otherwise it was a standard 64 with no internal changes from the classic snubnose model.
After the 128 failed to take the world by storm like the 64 did, Commodore toyed with the idea of producing a truly upgraded 64, dubbed the Commodore 65. This would have been similar to the Amiga 500, with built in 3.5" floppy disk drive and sound and graphics capabilities on par with the Apple IIgs. It was never put into production, however, and just a few prototypes were make before the project was cancelled.
Commodore then switched focus with the 64 as computer technology had passed it by. The old 8-bit architechture was superceded by the 16/32 bit PC compatibles and Mac/Amiga/ST 68000-based GUI machines. Commodore did see a market for the 64 hardware in video games, competing with the original NES which used a 6502 processor like the 64. The 64's innards were repackaged into the 64GS game system in 1990. This was a cut-down 64 motherboard containing only a cartridge slot and joystick ports - no keyboard or serial port was included. It was only released in Europe and failed in the market because even the proven architecture of the 64 was being obsoleted by the 16-bit Super Nintendo Entertainment System and Sega Genesis at this time.