Mono's implementation of ASP.NET AJAX is limited to the server components. Luckily the client-side library is effectively open source under the terms of the Ms-PL license (same one used by IronPython, DLR; it lacks the OSI stamp of approval, but it is effectively a FLOSS license).
A bunch of AJAX-enabled ASP.NET components are also being developed in an open source way. You can check out Microsoft's sampler here.
In other news, Mainsoft has also launched http://blog.mainsoft.com/blog, an aggregator for all-things Grasshopper, .NET on Java and Mono. Check it out!