I am making utility classes that will provide general methods for helping manipulate strings. I may also want one for arrays, math functions, etc. Should these be components? Vendors? Could I maybe make these into some sort of vendor package?
If they're general standalone libraries not tied to any particular step of the request cycle (controller, model, view), put them in app/libs/. You can import them using App::import('Lib', 'Foo').
Personally I have two or three handy array functions I always use defined in bootstrap.php, which is another place to put a small amount of global stuff.