If you have two triggers on the stack and your opponent responds to the first, does the second still resolve?

When two triggered abilities trigger at the same time, both are placed on the stack as separate objects, typically in the order chosen by their controller (CR 603.3). Once on the stack, they exist independently of each other.

If your opponent responds to the top trigger (or any trigger) with a spell or ability, that response goes on top of the stack. After the response resolves, the original trigger it was aimed at resolves next. The other trigger is still sitting on the stack beneath everything and will resolve in due course (CR 608.2).

Countering or otherwise affecting one trigger has no automatic effect on the other. Each must be dealt with separately. If your opponent wants to stop both triggers, they need separate answers for each (CR 603.6).

Concrete example: You control Guttersnipe and Electrostatic Field. You cast a Lightning Bolt, putting both "deal 2 damage" triggers on the stack. Your opponent casts Stifle targeting the top trigger (Guttersnipe's). Stifle counters Guttersnipe's trigger, but Electrostatic Field's trigger is still on the stack and resolves normally, dealing its 2 damage.

In short: stack objects are independent. Resolving, countering, or responding to one does not touch the others already on the stack (CR 112.7a, 603.3).