Hey,
Well, I know my question is like asking for favorite web framework or favorite programming language but any way, I'm asking for your opinion, your own stories and hands on experience.
What do you prefer, Maven or Ant + Ivy? did you try both of them?
How about Maven + Ant? I often use Maven to do what it does best - build and package a single module, whether WAR or JAR, and handle dependencies. I then use Ant to do everything else, such as handle the additional configuration files required by the app server (almost all of my development work concerns Java EE) and do deployment. Also I like Maven's default directory structure, though when I do a pure Ant project I tend to tweak that structure (I prefer a target/dist directory with the JAR or EAR file located there).
But then, I am not a Maven expert - I'm sure that someone well versed in Maven could get it to do what I do with my Maven + Ant combination.
Finally, there are some things that I tackle only with Ant, but then I am using it more like a scripting language than a build tool.
I'm going to add +1 to Peter's reply. I'm a fairly heavy Maven user but unfortunately Maven does not cover all corner cases, dropping back out to Ant can often help you resolve that.
So in short, Maven gives you a great solid base to start from (because it forces you to think about best practices) and Ant can help you get those nasty corner cases that Maven can't handle (yet).