JavaScript: 4 tokens (** based on broad interpretation of "assignment"!)##

Obviously my score of 4 is extremely generous/lenient!

To arrive at that score I've assumed "assignment" (worth 0 tokens in the question) includes such things as additive assignment, subtractive assignment, multiplicative assignment, and XOR-ing (^=) assignment

function f(a, b, c) {
  d = a;
  d -= b;
  d = d >= 0;

  a *= d;  //a = a if (a>=b), else 0
  d ^= true; //invert d
  b *= d;  //b = b if (b<a), else 0

  a += b;  //a is now max(a,b)

  d = a;
  d -= c;
  d = d >= 0;

  a *= d;  //a = a if (a>=c), else 0
  d ^= true; //invert d
  c *= d;  //c = c if (c<a), else 0
  a += c;  //a is now max(max(a,b),c)

  return a;
}

If those assignments actually count the score is 14 :)

JavascriptJavaScript: 4 tokens (** based on broad interpretation of "assignment"!)##

Obviously my score of 4 is extremely generous/lenient!

To arrive at that score I've assumed "assignment" (worth 0 tokens in the question) includes such things as additive assignment, subtractive assignment, multiplicative assignment, and XOR-ing (^=) assignment

function f(a, b, c) {
  d = a;
  d -= b;
  d = d >= 0;

  a *= d;  //a = a if (a>=b), else 0
  d ^= true; //invert d
  b *= d;  //b = b if (b<a), else 0

  a += b;  //a is now max(a,b)

  d = a;
  d -= c;
  d = d >= 0;

  a *= d;  //a = a if (a>=c), else 0
  d ^= true; //invert d
  c *= d;  //c = c if (c<a), else 0
  a += c;  //a is now max(max(a,b),c)

  return a;
}

function f(a, b, c) {
  d = a;
  d -= b;
  d = d >= 0;

  a *= d;  //a = a if (a>=b), else 0
  d ^= true; //invert d
  b *= d;  //b = b if (b<a), else 0

  a += b;  //a is now max(a,b)

  d = a;
  d -= c;
  d = d >= 0;

  a *= d;  //a = a if (a>=c), else 0
  d ^= true; //invert d
  c *= d;  //c = c if (c<a), else 0
  a += c;  //a is now max(max(a,b),c)

  return a;
}

If those assignments actually count the score is 14 :)