The simple answer is: yes, they are. And always have been. However, not even most of us here, who care particularly about video games, really realize this: the Video Game industry has done a great job of marketing their systems as "not computers." There are specific adaptations Video Game consoles have made that help them seem like they aren't just computers, so let's go over those.

1) Marketing. This is by far the most important component: imagine if Dell, for example, were to market a specific model of Computer they build as "The Lightning," instead of "Model AS-4233," or some such thing. They posted advertisements everywhere telling people to catch it. They hammered the name into people's brains, and emphasized the system's video game usage. I think pretty quickly, you'd see a lot of people referring to this as "The Lightning," and not as "a computer".  By giving each system a specific name, it gives them a feeling of permanence and stability. 

2) You can't upgrade Video Game systems at all. You can add on to them, a la the Sega CD or Xbox360 HD-DVD drive, but you will never, say, replace the 512 MB of RAM in a Xbox360 with a Gigabyte instead. 

3) Video Game systems have historically forsaken most computational functions besides video gaming in order to bring prices down. The most obvious example at this point and time is the Wii: it's less than half the price of the PS3 not just because of graphical inferiority, but also because it doesn't display movies (at all, not just blu-ray), doesn't play music, and so forth. This cuts down on production costs, and thus on price as well. 

4)  They plug easily into your television. Unlike most PCs, which require a bit of jerry-rigging to connect to most televisions, Video Game systems can go right home and right onto your main TV in your living room -- instead of connecting it to the monitor in your office. Like the first point, this is purely psychological, but unlike the first, it isn't a big selling point, just a small one.

If I've left anything out, please let me know -- but I hope it makes my point clear. Video game systems are computers, they're just brand-name computers that can't be upgraded, only play games, and plug directly into your television. That's it. 

Which brings me to my second point: both the Xbox360 and the PS3 are violating the rules above, and I think in both cases, it's to their detriment. The Xbox360 (especially with the now rumored Blu-Ray add on drive) is suffering from add-on disease, like the Sega Genesis before it: you can get an Xbox360 core, an elite, or a premium, and then you can buy a large number of add ons like the HD cables, the headset, the HD-DVD drive, and the (supposed) Blu-Ray drive. This isn't quite like upgrading your RAM, but it is annoying and "computerish" enough to get on some people's nerves. The PS3 breaks rule 3: it's trying to do so much, and at a greatly increased cost. The bulit in Blu-Ray player is the major factor in this. Here's a simple, hypothetical question: if Sony released a mouse/keyboard add on for the system, then added programs similar to MS Word and/or MS Office, a PS3 would be so close to just being a computer by function that none of us would know the difference. Seriously -- how many of you spend a great deal of time on your computer doing anything but using MS Word, surfing the web, playing music, watching movies, looking at photos, and playing games? I'd say those listed activities comprise at least 90 percent of my personal computer use. The additional price these extra features bring has clearly kept many people away from buying a PS3. 

So, there you have it. My overriding point, here, is this: video gaming companies have done such a great job of marketing their product that most of us don't even think of these machines as computers. But they are. Just slightly altered ones. 

no but they should be stand alones, although the power should be reckoned with, you should read my post on when enough is enugh!! http://www.vgchartz.com/forum/thread.php?id=1949&start=0#end

If we go for a classical definition, any device that is capable of executing a program qualifies as a computer. This generally implies the existence of some sort of registers for storing values, an instruction set for defining programs, and the basic infrastructure like the program counter, maybe a stack, generally I/O of some sort so you can see and influence what it's doing. But to the original poster's point, I think most people realize that games can be played on computers and game consoles are essentially stripped-down computers. It's more about the purpose and context of the application -- I don't want a computer humming away in my living room, and I don't want a game console taking up space on my desk. Blame it on marketing if you like, but the perception is that game consoles are toys for having fun and computers are tools for doing work. I think that perception maintains its consistency even if you're comparing a Commodore 64 to a Playstation 3. Which is why the computer is perceived as an investment that requires maintenance and might need repair or upgrade, and a console is regarded as cheaper and more plug-and-play.

 I absolutely agree with you, Ddobson. You succinctly said what I did. Seriously, it's very close to a synopsis.

Although I'm not sure I'd agree that most people know that a video game console is a stripped down, simplified version of a Personal Computer. A vague sense that it's a computer, perhaps, but not a concrete recognition that a video game system is just a few applications and hardware upgrade away from being a PC.  

The term computer is usually means a general computing device to most people.

Video games historically is not a "general" computing device, but with the last couple generations, the distinction is blurring.

Simply put it's a spectrum.  These days, pretty much everything contains a "computer", be it digital watches, cell phones, or traffic lights.  Just so happens gaming consoles use chips that computers also use, which makes them more general.

A word on terminology: the term "computer" used to refer to humans who compute.  Word meanings evolve, and for a word like "computer" obviously its meaning is in constant flux.  It's kind of pointless to argue what "is" and what "isn't" a computer.

slowly consoles are becoming inexpensive computers.. well the 360/PS3.. the Wii.. might be able to be counted if they enable support for a keyboard + mouse.

The line has been blurred with the ubiquity of silicon everywhere, so yep, based on strict definition they are computers. So is my Linux-powered toothbrush.