Can the Incredible Hulk die?
The simple answer is yes, but it varies how it is possible.
In the one-shot comic "Hulk: The End" written by Peter David, Hulk is almost invincible. He survives a nuclear holocaust when no one else does. Although, Bruce Banner is not invincible. He dies and hulk realizes he cannot transform without dying also. From the synopsis:
Suffering a painful heart attack, Banner realizes how much his punishment resembles that of Prometheus, the Last Titan; condemned to stay forever alive even while animals devour him, speculating that the Hulk's suffering is Earth punishing him for humanity's sins as the embodiment of the nuclear wars that destroyed Earth. As he dies, the Hulk's persona arises in his mind. [...]
The next morning, the Hulk somberly sits outside the cave, musing in his inner monologue: "Banner is gone...got rid of him last night." As he remembers the confrontation, he realizes that if he were ever to change back to Banner, he would die also.
In the Lou Ferrigno version of Hulk, there was a TV movie called The Death of the Incredible Hulk. Hulk falls from a exploding plane and dies on the ground. Although in true comic style, "there was talk of another Incredible Hulk television movie which would resurrect the character." Unfortunately, Bill Bixby (who portrayed Bruce Banner) dies before that ever happened.
In the comics Tales to Astonish #90 & 91, the Abomination is created and kills Hulk. He is revived shortly after though.
In the Old Man Logan comic series, Hulk kills and eats Logan. "Logan recuperates within Banner's stomach and bursts out, killing him." See below:
In Thor #73 (The Reigning Part 5), Thor kills the Hulk and others. Although, I believe at the end of The Reigning story arc Thor turns back time. This gallery has several pages from that issue, such as the one below. Thor also snapped Hulk's neck in a What If? issue that I couldn't find.
Other characters have supposedly killed the Hulk, such as Deadpool, Red Hulk (Rulk) and Galactus. But they were all in "what if?" type comics, and I couldn't find solid details online. I found evidence that Hulk killed Red Hulk (not the opposite), but this stands to reason if one hulk can die, the Hulk could die.