Do you want different user roles to have different Front pages when they login or go to the Home page?
The Front Page module (https://drupal.org/project/front) works very well for that. 18,109 reported installs at the time of this writing.
If you want token support, 7.x-2.4 and lower will need a patch: https://drupal.org/node/1786128
Front Page handles roles in the reverse order of what you have defined in the Role arrangement and creation page (admin/people/permissions/roles), so Admin role, then Authenticated, and then finally Anonymous role will be processed when implementing a custom front page.
Here's a screenshot of 2 roles, Authenticated and Anonymous.
As an example, for an e-commerce site and with token support, I can redirect a "customer" role to their Orders page.
More advanced users and cases will probably want to use Rules.