I agree with the post by brd6644 (and would have voted it up if I could). Especially his comment on logging. Using aspects for logging is more akin to tracing.
There are two podcasts on se-radio.net on AOP. The first, and interview with Gregor Kiczales, who has done a lot of research on AOP; the second, more recent interview with Christa Schwanninger and Iris Groher focuses on how AOP is used in practice. Both are worth a listen.
Finally, be careful in how you adopt AOP. Too much focus on AOP and you are concentrating on the platform rather than delivering business value. I have never been directed to use AOP by a test case. Aspects are something I would introduce during refactoring of an app to remove duplication.