[3-12] When is it right to use EVAL?

Hardly ever.  Any time you think you need to use EVAL, think hard about it.
EVAL is useful when implementing a facility that provides an external
interface to the Lisp interpreter.  For instance, many Lisp-based editors
provide a command that prompts for a form and displays its value.
Inexperienced macro writers often assume that they must explicitly EVAL the
subforms that are supposed to be evaluated, but this is not so; the correct
way to write such a macro is to have it expand into another form that has
these subforms in places that will be evaluated by the normal evaluation
rules.  Explicit use of EVAL in a macro is likely to result in one of two
problems: the dreaded "double evaluation" problem, which may not show up
during testing if the values of the expressions are self-evaluating
constants (such as numbers); or evaluation at compile time rather than
runtime.  For instance, if Lisp didn't have IF and one desired to write it,
the following would be wrong:

   (defmacro if (test then-form &optional else-form)
     ;; this evaluates all the subforms at compile time, and at runtime
     ;; evaluates the results again.
     `(cond (,(eval test) ,(eval then-form))
            (t ,(eval else-form))))

   (defmacro if (test then-form &optional else-form)
     ;; this double-evaluates at run time
     `(cond ((eval ,test) (eval ,then-form))
            (t (eval ,else-form)))

This is correct:

   (defmacro if (test then-form &optional else-form)
     `(cond (,test ,then-form)
            (t ,else-form)))

The following question (taken from an actual post) is typical of the
kind of question asked by a programmer who is misusing EVAL:

   I would like to be able to quote all the atoms except the first in a
   list of atoms.  The purpose is to allow a function to be read in and
   evaluated as if its arguments had been quoted.

This is the wrong approach to solving the problem. Instead, he should
APPLY the CAR of the form to the CDR of the form. Then quoting the
rest of the form is unnecessary. But one wonders why he's trying to
solve this problem in the first place, since the toplevel REP loop
already involves a call to EVAL. One gets the feeling that if we knew
more about what he's trying to accomplish, we'd be able to point out a
more appropriate solution that uses neither EVAL nor APPLY.

On the other hand, EVAL can sometimes be necessary when the only portable
interface to an operation is a macro.