If you are already using source control management (scm) such as subversion and a build tool like ant or maven that Hudson supports then it is not that much work to set up an automated build for the projects.
The first advantage you will have is very quick notification when someone commits something that breaks the build. If a project no longer builds from your scm trunk you'll know within minutes.
You haven't mentioned if you are using unit tests but if you are, you can also be notified as soon as one fails. You can make it so that every time someone checks in new code to scm the tests are all run and notification emails delivered if a test fails.
Not only can you see that it's broken but by viewing the build history you can see exactly what code changes occurred between a build that passed and one that failed.
I've never installed hudson from scratch but it has a nice web UI, and I've added builds for new projects to it in a matter of minutes.
These are the most obvious advantages but if you want to go further you can do some other neat things like add emma or pmd to analyse the code coverage and complexity of the proejcts over time. Any good developer should get a warm fuzzy feeling looking at graphs showing how your test coverage has increased over time.
If you are having versioning problems with some of your projects that depend on specific builds of some of your other projects you'll want to do 2 things:
1) Properly branch and tag your builds using SCM
2) Look at something like ivy to manage the dependencies.