A friend of mine claims (quite vehemently) that Apple was the first company to create a computer with a colorful case. However, I swear I saw ads years ago for colored PC cases.
What’s the Straight Dope?
Well, I can tell you that I had an olive drab PC many years ago, and I’d seen a rainbow of fruit flavors in stores in Korea. But I believe your friend is right in the sense that they were the first to use hip translucent plastic and mass market the things. After the iMac came out, EVERYTHING turned into translucent plastic. I have a goofy-green USB hub blinking in front of me now. Apple is to blame for that. 
I stil own a vintage PC, a Sol Terminal Computer that I built from a kit in 1975. The SOL-20 was famous for its bright blue case, with solid walnut side panels, and was the first all-in-one PC that included the keyboard in the case. All the other PCs of that era either came with no case (i.e. Apple 1) or came in square boxes with nothing but switches on the front so you had to add an external terminal (i.e. the Altair, which I should note, was also colored blue with metal trim).
I don’t recall when beige came to predominate, most of the early PCs were of varying case designs, but when the IBM PC came along, everything went grey and beige.
Picture of Apple 1 and Altair 8800.
Hey!!
I just posted about this the other day. Well, OK, it wasn’t on this exact topic, but it’s close.
Put it this way- I think these guys were way ahead of both Apple and the PC’ers. Take a look at a some of the gallery pages…
Well, australopithecus used berries to color
…(FAST FORWARD)…
and it was brought to Persia by the Mongols
…(FAST FORWARD)…
which was also used by Charlemagne when
…(FAST FORWARD)…
until Apple came out with the iMac
…(FAST FORWARD)…
Blame it on El Niño.
Cobalt had a machine that was both blue and cubic quite a while ago.
SGI and Sun machines have come in colors for quite some time.
I do believe Apple was the first to offer a choice of colors for a given model, however.
a few nitpicks:
The Cobalt Cube came out just after the Mac Cube, and far postdates the iMac.
The original Apple II came in two colors, beige and black. The “black apples” were sold only through Bell & Howell, primarily to schools but also to A/V users. The Apple II was the first personal computer to ship in an injection-molded one-piece plastic case.
Getting real picky:
However, an injection-molded one-piece plastic case, in basic black, was available as an option for the Rockwell AIM 65 in 1976. It converted a pretty motherboard into something resembling a carrying case for bowling balls.
This is completely false. The Cobalt Qube was shipping in 1998, a long time before the G4 Cube.
Of course the NeXT cubes were older still.
I gotta check mine for an exact date. I believe it was made in the late 70’s. It came in two pieces. The floppy drive unit is roughly the size of my current tower PC. The case is wood grain. The Horizon’s keyboard and monitor were a single unit-dark blue on the lower half and light blue above. When I first saw the Imac, I noted the (presumably coincidental) resemblance to the Horizon.