"So here's my question, how long does Apple support their computers? I'm worried that it will only be supported a very small time frame. I know that iMacs are different than iPhones, iPads...which have limited time frame suport [2-3 years], so spending $2000 on a computer concerns me."
You're going to get some "fanboy" replies to your question, and some more realistic ones. My reply (as a Mac user since 1987) tends toward the "realistic" side of things.
I've only had one iMac so far. It's a 2007 "white" Intel model, the last of the "white iMacs". I've used it modestly over the last 5 years, my "workhorse" is a 2004 g4 PowerMac tower that is still running (typing on that now).
No problems to speak of with the iMac in the years I've owned it, but to give you an example insofar as "support" goes, it will not run the upcoming "Mountain Lion" software release (OS X 10.8). I'm guessing there will be hacks to get it to run, but haven't seen one that's easily workable, yet (I expect that to improve as more is learned about ML).
Based on my experience and reports of others, about 5 years is "what you can expect" from an iMac, give or take. It's quite possible you might get a few more years out of it, and then again, you may experience a hardware failure in less time. One point of contention (particularly with the 27" iMacs) has been discoloration of the display, particularly in the corners, which seems to be "heat-related" due to the screen's proximity to heat-producing components directly behind it. This is a design constraint/limitation, not sure how Apple will address this in the future.
I've you're unsure about the longevity of the iMac, you might consider the Mac Mini line, particularly the midrange Mini or even the "server" model. The Minis (at least what I've heard) seem to have a pretty good service record. I will _guess_ that the next release of the Mini (which may come in summer/late summer/fall) will be a nice "jump upwards", with the Ivy Bridge CPU, better graphics, and USB3 (which will debut on all Macs this year). When it comes time to replace this old g4 (soon), I'm going to get a Mini to operate in its place; right now, the only question is which Mini that will be.