Jon Kern, one of the original authors of the Agile Manifesto, has written a good overview of Agile approach to software testing. In it he talks about mixing different kinds of tests - including manual tests - and testing techniques, and ends with a reminder that judgement is required about when choosing what to test and not to test: "The point is to use your brain!"
the aspect of "Agile Development" that comes to the fore [with regard to testing] is simply: 'Reduce the gap in time between doing some activity and gaining feedback.' Though typically couched in terms of discovering errors sooner, there is a positive side to this concept. You also want to discover you are finished (with a feature) as soon as possible!
Jon Kern is a software engineering evangelist, Agile Manifesto co-author, speaker, agile coach, practitioner and author. He works at Compuware which produces model driven development tools for Java and .NET.
More on testing: http://www.infoq.com/testing