  We study $d$-dimensional Conformal Field Theories (CFTs) on the cylinder,
$S^{d-1}\times \mathbb{R}$, and its deformations. In $d=2$ the Casimir energy
(i.e. the vacuum energy) is universal and is related to the central charge $c$.
In $d=4$ the vacuum energy depends on the regularization scheme and has no
intrinsic value. We show that this property extends to infinitesimally deformed
cylinders and support this conclusion with a holographic check. However, for
$\mathcal{N}=1$ supersymmetric CFTs, a natural analog of the Casimir energy
turns out to be scheme independent and thus intrinsic. We give two proofs of
this result. We compute the Casimir energy for such theories by reducing to a
problem in supersymmetric quantum mechanics. For the round cylinder the vacuum
energy is proportional to $a+3c$. We also compute the dependence of the Casimir
energy on the squashing parameter of the cylinder. Finally, we revisit the
problem of supersymmetric regularization of the path integral on Hopf surfaces.
