Like how the click() can be used to trigger a click event on an element, is there any way to simulate the typing of a string?
Are you looking for a way to trigger the events associated with typing or do you want to append text to a container so that it looks like someone is typing? If you're looking for the events, then @Nick is absolutely correct in suggesting the methods for triggering the event. If the latter, you'll want to use a timer to replace the text/html of the container with successive substrings of your text. You might be able to get a better effect by appending successive span elements containing each letter if the text is very long -- this would reduce flashing as the text gets replaced and the layout changes momentarily.
EDIT: I was going to add an example, but it turns out there's a plugin for that already: jTypeWriter.