Can Features package its dependencies? I have just created a Feature that has about 10 module dependencies.
I installed the feature on the target Drupal instance, and discovered that the dependencies were not included in the feature tarball. Is there a way to tell features to package dependency modules into the feature so that they will get installed along with the feature?
Or am I misunderstanding what the features module is supposed to do?
I think the latter is true, and you're misunderstanding what Features does.

Features takes any database-stored configuration (Views for example), and exports it to code.  The generated module is essentially just a package that then contains the code version of your configuration.  

For example, if you create a Feature containing a Blog content type, and a View that show all Blog articles in a list - the generated Feature is simply a module with that configuration stored in code, and exposed to Drupal.

If you want all of the modules packaged, you are looking more towards a distribution - which is a completely different kettle of fish.

To cut a long answer short, Features is a module builder - so as with any other module, dependencies must be retrieved seperately.