The Arf invariant of a knot is a Z/2Z valued concordance invariant. If the Alexander polynomial evaluated at -1 is equal to 3 or 5 mod 8, then the Arf invariant is 1, otherwise (if it is 1 or 7 mod 8) the Arf Invariant is 0. (Recall that the determinant of the knot is the absolute value of the Alexander polynomial evaluated at -1.)
The Arf invariant can be defined in terms of the classical Arf invariant of the Seifert form, reduced mod 2. That is, there is a quadratic form on the Z/2Z homology of a Seifert surface, given by computing the linking of a class and its push-off. The Arf invariant is 0 if a majority of classes have self-linking 0 and 1 if most classes have self-linking 1.
For proper links (all linking numbers even) there is the Robertello invariant. For an n-component proper link, use (n-1) bands to form a knot. Robertello proved that the arf invariant of the resulting knot depends only on the initial link. This invariant obstructs the initial link from being (topologically or smoothly) slice.
 Robertello, R. "An invariant of knot cobordism," Comm. Pure Appl. Math. 18 (1965), 543-555.