A general calculation of Casimir energies-in an arbitrary number of dimensi
ons-for massless quantized fields in spherically symmetric cavities is carr
ied out. All the most common situations, including scalar and spinor fields
, the electromagnetic field and various boundary conditions are treated wit
h the uppermost accuracy. The final results are given as analytical, closed
expressions in terms of Barnes zeta functions. A direct numerical evaluati
on of the formulae is then performed, which yields highly accurate numbers
of, in principle, arbitrarily good precision.