There was a Marriott iPhone app back in June of 2009. There doesn't appear to be a generic iPhone app for Marriott. There is a specific one for the Annapolis Marriott, and there is one for Renaissance hotels that requires a code prior to download.

Perhaps someone can shed some light on the old app. Not sure one is really necessary as long as you can get to their site. I made a number of reservations in the UK this past week on my iPad...