  We investigate generic properties (i.e. properties corresponding to residual
sets) in the space of subshifts with the Hausdorff metric. Our results deal
with four spaces: the space $\mathbf{S}$ of all subshifts, the space
$\mathbf{S}^{\prime}$ of non-isolated subshifts, the closure
$\overline{\mathbf{T}^{\prime}}$ of the infinite transitive subshifts, and the
closure $\overline{\mathbf{T}\mathbf{T}^{\prime}}$ of the infinite totally
transitive subshifts.
  In the first two settings, we prove that generic subshifts are fairly
degenerate; for instance, all points in a generic subshift are biasymptotic to
periodic orbits. In contrast, generic subshifts in the latter two spaces
possess more interesting dynamical behavior. Notably, generic subshifts in both
$\overline{\mathbf{T}^{\prime}}$ and $\overline{\mathbf{T}\mathbf{T}^{\prime}}$
are zero entropy, minimal, uniquely ergodic, and have word complexity which
realizes any possible subexponential growth rate along a subsequence. In
addition, a generic subshift in $\overline{\mathbf{T}^{\prime}}$ is a regular
Toeplitz subshift which is strongly orbit equivalent to the universal odometer.
