  For a very general class of weighted Fock spaces on $\mathbb{C}^n$, we give
necessary and sufficient conditions for a Toeplitz operator with a (not
necessarily positive) measure symbol to be compact. Furthermore, we show that
all compact operators are in the norm closure of the algebra generated by
Toeplitz operators with $C_c ^\infty(\mathbb{C}^n)$ symbols, and in the Hilbert
space setting show that all compact operators are in the norm closure of the
set of such Toeplitz operators.
