Strings in strong gravitational fields

String propagation in exact plane-wave solutions (with nonzero axion and dilaton fields) is analyzed. In these backgrounds, strings can undergo transitions from one state to another. Selection rules are derived which describe allowed and forbidden transitions of the string. It is shown that singular plane waves result in infinitely excited strings. An example is given of a solution whose singular properties are the opposite of an orbifold: it is geodesically complete, but still singular from the standpoint of string theory. Some implications of these results are discussed.