There are a few instances where her skills as an empath prove invaluable
In TNG: Faces of the Enemy, Troi's empathic ability helps her to instantly determine that the Romulan vessel is walking into a trap. As a result, she has the freighter destroyed and protects her "cargo", an enormously valuable defector.
TROI: (softly) He's lying. They have no intention of keeping their
N'VEK: Are you certain?
In TNG: Shades of Grey, Troi uses her powers to determine Riker's emotional state. That allows Pulaski to stimulate only those memories that elicit a dampening effect on the organism
PULASKI: The growth rate has definitely slowed. What is he feeling? Can you tell?
PULASKI: Just the opposite of before -- and it's having the opposite effect on the infection.
and in the film TNG: Nemesis, she uses her empathic skills to detect the location of the Scimitar, arguably saving the Earth and the whole damn Federation
DEANNA: Captain -- I might have a way to find them.
DEANNA: The one thing he may have forgotten in the course of battle: me.
PICARD: Make it so.
She quickly goes to Worf at tactical.
Deanna concentrates furiously, eyes closed. She stands with Worf, her
hand slowly moving his over the photon torpedo targeting display.
Deanna continues to move Worf's hand over the targeting display. She
is sweating, panting for breath, concentrating fiercely.
Her eyes snap open --
Worf instantly fires a full volley of photon torpedoes.
A full spread of photon torpedoes shoot through space. And connect! A
series of devastating impacts -- and the Scimitar's cloak fails!