Page manager redirect (PMR) is a nice little module that allows you to specify new or existing paths and redirect them to wherever you want.
Using the same mechanisms that panels uses PMR allows you to set up conditions and contexts to control where you redirect to.
There is a submodule of examples included with PMR, please enable it and take a look at some of the example redirects, by going to the Page Manager admin screen. In Drupal 7, this is found at http://MYSITE/admin/structure/pages or Administration >> Structure >> Pages, or in Drupal 6: http://MYSITE/admin/build/pages or Administer >> Site Building >> Pages. (Replace MYSITE with your website's domain)
Here's a really quick explanation of how to set up a redirect (further documentation is needed, see http://drupal.org/node/842944):
2) Create your page/variant, and select Redirect (rather than Panel) on the first screen in the create variant wizard.
3) Set up any contexts or selection rules you need (We won't provide documentation for this, as this is something provided by CTools Page Manager - find a good screencast that walks you through these concepts)
4) Finally, enter the path (and fragment/querystring) that you want to redirect to. You may use substitutions for things like a node ID or user name, which are defined on the contexts tab.
Since this module is made obsolete by the HTTP Response plugin that is now included with CTools, this documentation will probably not be expanded much more.
If you have specific questions about functionality in PMR that isn't in that plugin, then ask in the comments below.