There are at least two kinds of design patterns in Ajax: 1. usability/workflow design patterns 2. Software design patterns
The two main bodies of literature on 'Ajax Design Patterns' are Michael Mahemoff's wiki, and subsequent book of that name by o'Reilly (http://ajaxpatterns.org), and Bill Scott's stuff at Yahoo! developer site (http://developer.yahoo.com/ypatterns/). Both of these talk principally about useability & workflow patterns, along with some discussions of request-response/comms patterns.
I discussed software design patterns in 'Ajax in Action' quite a bit, and more recently at a talk that I gave at QCon in London. The names here will be familiar - Observer, Model-View-Controller, Strategy, etc. - straight from the Gang of Four.
The interesting thing to me about applying design patterns in JS is that most of the literature has been on heavily OO languages - C++, Java, C# - whereas JS is muuch more aligned with functional programming. Hence, one approaches the __implementation__ of familiar patterns a bit differently.