What is the convention for sign of rotations in three space? When performing rotations in three space, is a rotation from x to z considered positive or negative? How do you determine whether similar rotations in three space are positive or negative?
 A: It can be positive or negative depends on the "direction" of your rotation axis.
The convention is the right hand rule.

If you point your thumb in the "direction" of your rotation axis and
  you index finger to the direction of the $1^{st}$ vector. If you can
  point your middle finger to the direction of the $2^{nd}$ vector, then
  the rotation is considered to be positive. If not, then the rotation
  is considered to be negative.

In ordinary $\mathbb{R}^3$, the "positive directions" of the 3 axis is setup such
that if you rotate the vector in "positive direction" of $x$-axis with respect to
the "positive direction" of $z$-axis for $90^{\circ}$, you get a vector in the
"positive direction" of $y$-axis.
If you attempt to rotate the vector in "positive direction" of $x$-axis with respect
to the "positive direction" of $y$-axis for $90^{\circ}$, you get a vector in the
"negative direction" of $z$-axis.
So the answer to your original question is "negative" when you measure your rotation with respect to the "positive direction" of $y$-axis.
Sound confusing and hard to remember? Same to me. When in doubt, I always use my right hand to figure out the "sign" of a rotation.
