At this day and age there is no reason to continue using Ant. Ant was a great tool for its time but this time has passed.
There are basically three build tools that can replace Ant: Maven, gradle and Buildr.
It is important to be able to continue using existing Ant scripts and custom tasks alongside the new tool. There is a multitude of useful open-source custom Ant tasks and with Ant being a de-facto standard for years, many development shops built vast libraries of Ant scripts and custom tasks.
Out of all three, Gradle has the best integration with Ant. It allows for using existing custom Ant tasks pretty much without any changes. It also allows for importing Ant scripts into Gradle build script. Gradle tasks can even depend on Ant targets (and vice versa). There is also easy access to Ant properties.
The bottom line, for any Ant shop, there is really nothing to loose from migrating to gradle. The benefits though are substantial:
What about Buildr and Maven?
Buildr provides some integration with Ant but it's certainly not as sophisticated as gradle's. And Maven is simply not a scripting tool in the same way Ant or gradle are, it is declarative as opposed to procedural (there is, of course, a blurry line between these two characteristics -- gradle could be made quite "declarative-like" via the use of plugins and Maven allows for invoking Ant tasks in a "scripting" fashion). So migrating complex Ant build scripts to Maven could be quite a complicated affair oftentimes involving developing custom Maven plugins.