I wanted to attach a fairly large number of variables (fields) to each user's profile, and the UI for displaying and updating (editing) "that many" variables was not to my liking.
At the moment (in 4.7, anyway), profile variables can be put into "categories" (apologies to jaza and bdragon, but that is the "official" description of the way that profile fields are divided into separate and distinct groups). When a user profile is edited, the various categories are displayed as links near the top of the first edit screen, with the first edit screen focused on the "account settings" category. Those with user administrative privs can add additional profile fields and each field can (actually, must) be placed within a category. I believe that there are no restrictions on the number of profile fields or the number of profile field categories, although I certainly haven't stress tested it.
The "edit user profile" UI currently loads a separate page for each category. That separate page lists all of the profile fields associated with that category, in the order specified by the normal Drupal weight/alphabetization mechanism. There is no ability to group the fields in a fieldset.
I have a simple module that allows those with user adminsitrative privs the ability to assign each profile field to not only a category, but to a fieldset, as well.