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.
This may be a bit late, but if you are using drush (the command line Drupal tool), the dependent modules will be downloaded when you enable the feature.
So if you have a feature called "MyFeat" which is dependent on modules A, B and C, you can copy the MyFeat folder to the target site (at sites/all/modules). Then from the websites/myDrupalSite directory, run the command "drush en MyFeat". Drush will detect the dependencies and ask if you want to download A, B and C.
May be not as elegant as Distros or Apps, but works for me and hope this helps you as well.