We seem to be totally spam free now.
We require users to register an account before they post. As part of the process they have to type in a code from an image, which is designed to be hard to read automatically. These things are known as CAPTCHAs
In phpBB3, which is the software we use, you can turn this on in the admin control panel under General / Board Configuration / Visual Confirmation Settings.
Other forum systems should have a similar feature available somewhere, though you might need to upgrade it or find some add-on to do it.