I think a good example might be ME2 in some ways. On Normal everything got hurt by everything and all is well. Above that , you had to defeat Shields and Armor differently and it added a new layer to strategy and how you played.
When a game offers tight controls, fair game mechanics and an arsenal of user friendly options to dispatch objectives, that’s when I tend to jack up the difficulty.
An excellent example is Saint’s Row 3. Volition also did well with Red Faction Guerrilla but I seem to remember most people putting it on easy, which I thought was a damn shame.
A bad example is Call of Duty. Going through the campaign on Veteran allows me to understand why many gamers are burned out on challenging experiences, especially since the COD formula has not changed in many years and perhaps references the genre’s previous standards.