Analog (3×5) approach
Given two cards that I want grouped together, I would put them down, either directly on top of one another, or positioned in an overlapped way, to indicate grouping. I might create a ‘group name’ card, preferably in a different color, that I can use to understand how the stories are related without having to read them.
Usability: High Downside: finding cards of a different color? Maybe, but running out of desk space may be the only down side

Ideal Digital Tool
If I select some number of story cards and then right-click on one of them and select ‘Group’, I would be prompted to give the group a name and a description, and perhaps be shown the list of selected stories to be made children of the new group object. I could take things out of the list with a click, add new stories right then and there, or search for additional ones to add. Upon clicking Ok, the new grouping record will be created, with the same parent as the selected record, and all of the selected stories made children of the new record.
Usability: High Downside: some of the additional functionality may be distracting to the basic use case, for some users

AgileOnDemand
Click Add on the drop-down, select Epic, then create the new epic. Then, drag and drop the stories to their new home.
Usability: Medium-High Downside: can’t drag and drop more than one at a time to re-parent, can’t have more than one level of grouping.

VersionOne
Create a new Feature Group, giving it the appropriate parent. Find the stories, check the checkbox next to them, then select the button at the top of the list and select Move to Feature Group. Select the correct feature group, and save the changes.
Usability: Medium Downside: more steps than is really necessary

Excel
Make sure you have a ‘group’ column. Put the same value in that column for all stories that you want in the same group.
Usability: Medium-High Downside: gotta type out the name, then copy/paste in order to avoid typos. Does not allow more than one level of nesting, per se.

Mingle
Create a new Epic, add it to the Feature tree, then filter for the stories you want to be added to it. Drag them to the epic.
Usability: Medium-Low Downside: not intuitive, and subject to some strange restrictions that I never did figure out

Rally
Create a new user story to be the group object. Make a note of its ID. One at a time, go in to the existing stories, edit them, and select the Parent field, click the looking glass icon, type the ID in the search box and click Search. Click Choose to apply the selection as the parent. Save the changes and go on to the next. If you didn’t create the group object as a child of the group that you wanted it to be a part of, you have to follow the same procedure for that.
Usability: Low Downside: clearly not designed with changing the hierarchy in mind.

Usability Comparison Summary on a scale of 1 to 10