Addressing the Wii part of the question.
As previous answers showed, there are 2 factors in consideration when emulating:
the hardware present at the console and the software present at your PC.
A Wii has the following specs (taken from Wikipedia ): CPU: IBM PowerPC "Broadway" (Single-Core @ 729MHz) Graphics: ATI "Hollywood" (@ 243 MHz) As you can see, in terms of processing power, a modern PC clearly surpasses a Wii.
Hence, it is possible to emulate Wii on a PC.
But this just opens the possibility.
In order for this to become a reality, one needs to write specific software.
Why?
The reasons are too complex to discuss at Arqade but short story the hardware of both console and PC don't talk the same language, and the emulator ends up being a translator program between your PC and the software made for Wii.
The complexity of such program increases as the complexity of the console increases.
As the Wii is comparatively simpler than the XBox or the PS3 systems, there exists some emulators for it.
XBox and PS3, however, are slightly more complex systems.
The XBox in particular is based around a standard PC.
Microsoft however made several modifications to the underlying systems and issued custom hardware.
This, coupled with the difficulty of reverse-engineering all the processes involved and translating them to a PC, makes the existing XBox emulators more of experiments.
The reasoning I use here for the original XBox can be expanded to XBox 360 or the PS3.
gaming.stackexchange.com/users/54659/Doktoro Reichard
As of yet, there is no PS3 or Xbox 360 emulator that can run games.
The things you find online are either a hoax, viruses or scam, so do yourself a favour and don't download any of these programs (especially if they are linked in a youtube video).
gaming.stackexchange.com/users/49182/5pike
There are Xbox 360 and PS3 emulators in development currently: Xbox 360 Emulator Project - GitHub PS3 Emulator Project -
GitHub PS3 and XBox
360 emulation is tough but not impossible.
The two emulators are very much 'work in progress' but soon they will run some games (the Xbox 360 project is further along).
gaming.stackexchange.com/users/67924/aniruddh saxena
Emulating a PS3 is a difficult task because it's main processor, Cell, resembles a modern GPU more than a regular CPU.
There are several slices of RAM which are only accessible by their respective cores and the main overwatch core, which also communicates between peripherals and the GPU.
This contrasts with normal PC processors where cores access the same memory and (with some considerations) are completely transparent to any executable code.
From there emerges the problem that PS3's code cannot be just translated on the spot automatically, meaning that whole processor has to be simulated .
In addition to this, some games on the PS3 use output from its GPU for other computations, so that part of the console would have to work like a real thing as well , which just deepens the issue.
This could potentially be solved with a GPGPU approach, given that the hardware has sufficient space to store a shader which works just as Cell's core does.
As of now, the emulator is mostly proof-of-concept.
gaming.stackexchange.com/users/68403/transistor09
I agree with @5pike`s answer but want to make a small addition.
First, why this happens.
Even today Xbox 360 and PS3 are pretty decent pieces of hardware.
To emulate those one will need insanely powerful PC and people willing to dig into those propietary consoles and write complex emulation software (both consoles have unique gaming-oriented hardware).
But not all is lost, actually.
It`s not
that
just you want to play those games, MS and Sony want you to play them too (and pay for them)!
So the work is in progress and the first actual solution from Sony was already announced: Playstation Now .
It`s
a streaming service that allows to play PS3 (and some other) games on different devices.
That does not include PC yet, but Eventually the service will expand beyond PlayStation platforms and Sony devices, allowing you to stream PlayStation games across a broad range of Internet-connected devices.
So my take on the question is the following: as long as Xbox360 and PS3 remain worthwhile platforms, our best bet for playing their exclusives are services from Sony and MS themselves.
They are not here yet, but coming.
As for independent emulators and such - I just don`t see it happening, not for a long time.
But that`s only my opinion anyways =)
gaming.stackexchange.com/users/62507/icebat
I'm a guy that only plays on PC, but there are some really decent games on Xbox 360 and PS3, that are made exclusively for these platforms.  I was wondering if it's possible to emulate consoles of that generation on a PC? If so, what software would I use? What are the hardware requirements?
Is it possible to emulate an Xbox 360 or PS3?
gaming.stackexchange.com
<emulation>
gaming.stackexchange.com/questions/150237
gaming.stackexchange.com/users/64410/Jutschge
There are Xbox 360 and PS3 emulators in development currently.  Emulating a PS3 is a difficult task because it's main processor, Cell, resembles a modern GPU more than a regular CPU.   While it is a difficult task, it seems that there are currently emulators capable of playing console games, in development.
A user is implying that there are emulators in development. While few other people are saying that it is not easy to emulate consoles.