The present invention is directed to molecules, such as monospecific antibodies and bispecific, trispecific or multispecific binding molecules, including diabodies, BiTEs, and antibodies that are capable of specifically binding to "Disintegrin and Metalloproteinase Domain-containing Protein 9" ("ADAM9"). The invention particularly concerns such binding molecules that are capable of exhibiting high affinity binding to human and non- human ADAM9. The invention further particularly relates to such molecules that are thereby cross-reactive with human ADAM9 and the ADAM9 of a non-human primate (e.g., a cynomolgus monkey). The invention additionally pertains to all such ADAM9-binding molecules that comprise a Light Chain Variable (VL) Domain and/or a Heavy Chain Variable (VH) Domain that has been humanized and/or deimmunized so as to exhibit reduced immunogenicity upon administration of such ADAM9-binding molecule to a recipient subject. The invention is also directed to pharmaceutical compositions that contain any of such ADAM9-binding molecules, and to methods involving the use of any of such ADAM9-binding molecules in the treatment of cancer and other diseases and conditions.