What qualifies a valid private key? The title pretty much sums up the question - say (for instance) I have a string of letters or numbers committed to memory, how hard would it be to convert that into a private key? Or similarly, how hard would it be to construct a private key based upon a sentence, mnemonic or otherwise?
Check out http://brainwallet.org/ for an example.

A bitcoin private key is just a 256-bit number. Any algorithm that can convert arbitrary text to a number of that size ought to do.

A rather simple algorithm would be to consider your string as a base 63 number (a-z, A-Z, 0-9 and spaces) and write in binary, take the number modulo 2256, and write in hex.

Or, you take the base 63-to-binary number, raise it to the power ten, bit shift left 20 times, multiply by 8, add 4, bit shift right 50 times, take modulo 2256, convert to hex, and you have a private key.

Or whatever. Try to make it so that the number generated before you calculate it modulo 2256 is much larger than 2256. Otherwise, many of your generated addresses will just be a bunch of zeroes followed by a relatively short hex string.