The definition of a TuringMachine includes the idea of a translation table, a symbol dictionary, and commands to move the tape head left or right (or builtin to the commands for read or write).  What is the simplest Turing machine conceivable?
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Define the TuringMachine thusly:  A tape, a wheel to move the tape FORWARD or REVERSE, an overwrite head to READ or WRITE symbols from or to the tape, and a translation table or function to transform the symbol into another.

''Anyone want to take a crack at it?''

Then a 1-bit adder with carryover allowing arbitrary length (but then, how to specify data vs. instructions?)
 consisting of a move (forward: 1, reverse: -1), a binary symbol (1,0), and a transition function ''f''.  Such can then be specified with a tuple of (move (1 || -1), symbol: (1 || 0), transition function: NAND):

Two options.  Define a word size, built into the r/w head that always moves a fixed amount on every READ.  Or, a special character could be used indicating separate words of arbitrary length.

* A computer without a program (0 bits long) is in the HALT state.
* The 1-bit program "1", moves one square FORWARD and reads the symbol there and continues.  The program "0" outputs a 0 and halts.
* The 2-bit program "00" stops .... jumps, adds, comparison, datasize definition... 

MarkJanssen,
Credit of NAND machine as the (untested) simplest TuringMachine to StephenWolfram. 
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See also GeneralPurposeComputer.