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.
Update
Yes, drivers have been published that will allow you to run on PC, hence, no need for any third-party software! [Source]
You can download the drivers for different build by using the links below or from Major Nelson's post I linked above as source.
Original dating back before 6 June 2014
No. The communication protocol the One controller uses is different from the communication protocol the 360 controller uses. This was needed to make several improvements such as reduced latency and more support for state messages for giving the console more control over the controller's state (it will put the controller in a low power state if you are not holding it).
But as you noted, all these improvements come at a cost. Until the time that someone comes up with a driver for the controller to be used on PC, there is nothing you can do. As X Padder relies on the protocol in use, it too won't be able to solve your issue. That being said, there supposedly is already a driver but because the protocol is likely protected by a patent, the driver would infringe on it. You can read some about it on this US Gamer article.
Best Answer
To the best of my knowledge such software does not exist. Most of the hacking work in the area is in making gamepads do keyboard like things, rather than emulating gamepads with keyboards.