If a spell is countered and never resolves, do 'whenever you cast' triggers that already fired still resolve?

When you cast a spell, it goes on the stack. Any abilities that trigger on casting — such as "Whenever you cast a spell..." — trigger at that moment and are placed on the stack on top of the spell (CR 603.3). These triggered abilities are completely separate objects on the stack from the spell that caused them.

If an opponent then counters that spell, the spell is removed from the stack and never resolves (CR 700.7, 701.5). However, the triggered ability is still sitting on the stack as its own independent object. Countering the spell does nothing to the trigger — there is no rule that says a trigger is countered if its source spell is countered.

The trigger will therefore resolve normally when it reaches the top of the stack. This is often called "the trigger still goes" in casual play, and it's an important strategic consideration when dealing with cast-triggered abilities.

Concrete Example: You cast Guttersnipe's ability isn't relevant here, but consider Electrostatic Field — or better: you control Aetherflux Reservoir and cast a spell. The Reservoir's "you gain 1 life for each spell you've cast this turn" trigger goes on the stack. Your opponent counters your spell with Cancel. The Reservoir's trigger is still on the stack and resolves normally, so you still gain the life.

The key principle is CR 603.3: a triggered ability goes on the stack as soon as it triggers, and its resolution is independent of the spell or permanent that caused it to trigger, unless that trigger is itself somehow countered (e.g., with Stifle, CR 117.5).