Roll the Alphabet into a Spiral
Logo, 129 87 bytes

Graphical solution, implemented as function

This was built on Calormen.com's Logo interpreter.  The S function takes the number of characters as a parameter and draws them in a spiral.  The T function outputs letters upright to prevent them from rotating with the spiral..  I decided that it looked nicer (and golfed out 42 bytes) to omit correcting the letter orientation.  I also tightened up the spacing which did not change the byte count.  If you were to actually roll up an alphabet, it would look more like this anyway.

Updated Version (letters roll)

TO S:r
PU IF:r[REPEAT:r[LABEL CHAR((REPCOUNT-1)%26)+65
RT 99/SQRT(REPCOUNT)FD 12]]END


Invocation

Invoke as follows: S iterations

Sample output

S 1000




Old Version (letters always upright)



TO T:l:h
RT:h
LABEL CHAR(:l%26)+65
LT:h
END
TO S:r
PU IF:r[REPEAT:r[T REPCOUNT-1 90-HEADING
RT 95/SQRT(REPCOUNT)FD 15]]END




Old output removed to save space.  See it here.