There's the common misconception, with some gamecube games, that they simply differenciated between analog and digital press, when, in reality, they used the full analog range.
(3 examples: melee, f-zero gx, sunshine)
Melee
Melee used the full analog range for its shield. By pressing the trigger (R or L) as slighty as possible, you would get the light shield (big and with a light color). By pressing the trigger (R or L) all the way down, you would get the regular shield (small and with a strong color).
So, starting from a light shield, as you holded the trigger further down little by little, your shield would keep getting smaller and smaller (you can see this as it happens), and going from a ligher to a stronger color, until it reached its minimum size (regular shield).
The other way around, starting from a regular shield, as you released the trigger little by little, your shield would keep getting bigger and bigger (again, you can see this as it happens), and going from a stronger to a lighter color, until it reached its maximum size (light shield).
F-Zero GX
F-Zero GX also used the full analog range (same as melee), but not just for a particular mechanic (like melee's shield), the whole game was build around it.
Each time you pressed one of the triggers in GX (and you were constantly doing so), it had an effect on the ship, how much, depended on how further down you were pressing the trigger/s.
You can easily test this by putting your ship on the center of the track, and holding both triggers to the same degree. One trigger shoud cancel the other, so your ship will remain in place. However, if you press one of the triggers even a bit further down that the other, your ship will move into that direction instead.
Super mario sunshine
The gamecube triggers were analog, yet they could be "clicked", like a button, if you pressed them all the way down.
Even though some games, like sunshine, did asign a function to the "click", it's main function was to give feedback to the player. In both melee and GX, clicking the trigger (digital input) and holding it down but stopping right before it clicked (max analog input), would give you the same value. So, max analog input = digital input.
In sunshine, the difference betweeen a digital and an analog press, was that, with an analog press, you were free to move mario with the analog stick, while spraying water at the same time, while, with a digital press, mario would stand still, and you would control were you aimed the spray of water with the analog stick.
The amount of time you were able to spray water, without losing pressure (therefore having to release and press the trigger for water to start coming out again), dependend on how further down you were holding the trigger.
Water lasted for around 5 seconds for both a digital press and a max analog press. For an analog press, the less further down you were holding the trigger, the less time water would last. If you were just barely pressing the trigger, only little drops would come out of fludd (there wouldn't be enough pressure for water to come out).
Conclusions
Without analog triggers, we would have the triggers as a digital input only (as if, each time you pressed one trigger in the original melee, GX or sunshine, you could only press it all the way down!!). All the sensibility of the analog triggers would be lost.
