How can I get FileZilla to ignore folder or files (like .svn or CVS)?

In FileZilla 3+ , click on the "filter directory listings"* button on the task-bar for a listing of existing filters to apply, edit, or add your a custom filter.

* it's the right-most button (with three arrows) in the middle-row in (image from http://wiki.filezilla-project.org/Using )

Detailed info on FileZilla filters

Click on View -> Filename filters (Filezilla 3.3)

For Filezilla 3.14 this option is under: View -> Filename filters...

Here is the dialog (with GIT, bower_components and node_modules custom rules):

As you can see SVN exclusion is now available by default. GIT and others has to be added manually with Edit filter rules... button.

Here is how rules editor looks (with GIT rule as an example):