What games? Most of them tend to get difficulty wrong: "this guy requires 3 headshots instead of 1!" It's better when the difficulty shows itself as more enemies, or stronger enemies, etc.
Off the top of my head, Bioshock: at lower difficulties, I found it easy to run through the game guns blazing; at higher difficulties you need to use your skills and the environment to your advantage. When 3 head shots are unviable or a drag, have you tried setting the enemies up the bomb?
Another example is Dungeon Defenders, where strategies differ dramatically (as in almost 100%) in the later stages of the game -- which in this case just means same levels, stronger enemies. Baldur's Gate (2, particularly) also was much deeper when it was difficult, forcing you to think more tactically to win fights. The list goes on and on.
The MGS series is a good example of a game series that scales difficulty well; the enemies are stronger AND work together better as a team, will hunt you better, etc.
Another example is Dungeon Defenders, where strategies differ dramatically (as in almost 100%) in the later stages of the game -- which in this case just means same levels, stronger enemies. Baldur's Gate (2, particularly) also was much deeper when it was difficult, forcing you to think more tactically to win fights. The list goes on and on.