Quine / Reverse Quine

CJam, 17 16 bytes

{`"_~"+Wq~g#%}_~

Test it here.

A fairly straight-forward modification of the standard quine. Other solutions for 17 bytes:

{`"_~"+q~{W%}&}_~
{`"_~"+q~!2*(%}_~

If I can assume that the input is only 0 or 1 (as a stand-in for a boolean, which there is no dedicated type for in CJam), I get 15 by omitting the g:

{`"_~"+Wq~#%}_~

Explanation

{`"_~"+  e# Standard generalised quine framework. Leaves the source code on the stack. 
  W      e# Push a -1.
  q~     e# Read and evaluate input.
  g      e# signum, turning truthy values into 1 (leaving 0 unchanged).
  #      e# Power. -1^0 == 1, -1^1 == -1.
  %      e# Select every Nth element: a no-op for 1 and reverses the string for -1.
}_~

Pyth, 17 bytes

_WQjN*2]"_WQjN*2]

A straightforward modification of the standard Pyth quine.

Gol><>, 9 bytes

'rd3*I?rH

I feel a little awkward posting this, since we already have ><>, Vitsy and Minkolang answers. The only additions to the standard quine are I (read integer input), ? (execute next if truthy) and r (reverse stack).

Try it online.