Data Recognition Software is that which recognizes PlugAndPlayData [paPd] or has been enabled in such a way as to be able to decode what kind of data it is looking at when it receives it. It would also have the intelligence to know whether it could handle/display/manipulate the data, as well as the ability to shift the data to a program that could.
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Questions: Does such software now exist? Would it be an impossible task to develop such a family of software? Would such software be desirable or needed? 

Yes, data recognition software does exist, and it's therefore not impossible, and it presumably exists because it's desirable and needed.  An example of data recognition software would be a Unix shell that reads a shebang before deciding which interpreter to use on a script file.  Perhaps the original poster can propose some concrete data recognition techniques, and then we can comment upon them?  Thanks.  -- SteveHowell

Note: DataRecognitionSoftware will also be able to operate in the background, operating on each and every designated file in your system, making it possible for the phrase iKnowIPutItSomewhere to be replaced with hereItIs. 
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Some browsers attempt to pre-scan a file to see it's type. A good example is the geocities trick of making .gif and .jpg files to .txt files because geocities doesn't allow storing of "images". However internet explorer will look at the file's first few bytes and load it as an image anyhow.

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Related
* DataRecognitionFeatures