  For various values of n, d, and the phase space dimension, we construct
simple examples of Hamiltonian and reversible systems possessing smooth
d-parameter families of invariant n-tori carrying conditionally periodic
motions. In the Hamiltonian case, these tori can be isotropic, coisotropic, or
atropic (neither isotropic nor coisotropic). The cases of non-compact and
compact phase spaces are considered. In particular, for any N no less than 3
and any vector omega in R^N, we present an example of an analytic Hamiltonian
system with N degrees of freedom and with an isolated (and even unique)
invariant N-torus carrying conditionally periodic motions with frequency vector
omega (but this torus is atropic rather than Lagrangian and the symplectic form
is not exact). Examples of isolated atropic invariant tori carrying
conditionally periodic motions are given in the paper for the first time. The
paper can also be used as an introduction to the problem of the isolatedness of
invariant tori in Hamiltonian and reversible systems.
