We call an abelian variety over a finite field isolated if it admits few (rational) isogenies to other abelian varieties. The motivation for isolated varieties comes from elliptic curve cryptography, where the discrete log problem can be transfered between elliptic curves by isogenies. By a the Honda-Tate theorem, counting the number of isolated abelian varieties reduces to counting certain algebraic integers in complex multiplication fields. An abelian variety is super-isolated if the isogeny class contains a single isomorphism class. Our main result is that if g ≥ 3, then there are finitely many such varieties. Moreover, we give some heuristics for the number of super-isolated elliptic curves and abelian surfaces.