Free Mac database software similar to FileMaker
I feel your pain.  I've not found a single app equivalent to MS Access for the Mac.  There are some decent online services like Zoho Creator (free) and TrackVia (not free) but if you MUST have something very close to Access or FileMaker installed on your Mac natively, I can offer the following suggestion.


On the Mac, you can install and run MySQL.  That'll be your database engine. Installation is beyond the scope here but there's tons of help via Google search.  Alternatively, you can use a separate computer or virtual machine (on your local network) with MySQL installed.
To design new MySQL databases like a pro, download and install the free MySQL Workbench.  http://www.mysql.com/products/workbench/
Building reports as good as FileMaker's or MS Access was a difficult find for a long time until I ran across the free Business Intelligence and Reporting Tools (BIRT) built into versions of Eclipse.  I opted for the development kit version - an enormous 220 meg download, but worth it. Check into it here: http://www.eclipse.org/birt/phoenix/ 


BIRT can connect to a variety of data sources and is intended as a Java application reporting tool, but it will also render/export reports in a lot of formats including PDF and DOC.  It's every bit as good as the report builder in MS Access.

PLEASE NOTE: BIRT requires a pretty significant learning curve but you will not regret it.  The thing blows my mind all the time because it is so mature of a product.  Like it knows what you want to do. There's lots of tutorials for BIRT on the Eclipse page above.  You'll need them.

If you desire to use a BIRT defined report in a web application, good luck.  I'm not very fluent with the Java web platform. I just haven't had the patience or need.

All in all, this combination of MySQL, Workbench, and BIRT is the closest thing I've come to that makes me feel like I have a good native database on the Mac.  

All the best.