One really nifty piece of code that I associate id-software with is the 0x5f3759df hack. Though it was probably known before, Hakmem would be the first place to look.
I am sure there are many more such bit twiddling and magic number hacks, but nothing quite as useful to me than this magic to compute the reciprocal of a square root. The only other floating point operations that comes up this frequently in what I do are log and exp.
In my day to day coding (not that I code every day, far from it) I have nothing to do with game engines, yet inverse square root shows up in almost every corner (pun intended) in the vector manipulation code, for example in finding the cosine similarity between two documents.
Does not work for double precision, 64 bit, and nothing I write is so performance critical that it demands the use of this trick, but its still fun
float Q_rsqrt( float number )
{
long i;
float x2, y;
const float threehalfs = 1.5F;
x2 = number * 0.5F;
y = number;
i = * ( long * ) &y;
i = 0x5f3759df - ( i >> 1 );
y = * ( float * ) &i;
y = y * ( threehalfs - ( x2 * y * y ) );
return y;
}