Poet Kenji Miyazawa (1896-1933) wrote about himself on the verge of death in his poem "Speaking with the Eyes." Unable to talk due to blood gushing from his lungs, he tried to tell his attending doctor with his eyes that, despite the suffering, he knew that he was departing to a better place. (He didn't actually breathe his last then.)
To Miyazawa, a devout Buddhist, dying was but a passage into another realm of existence. A word for "dying" that expresses this is 他界する (takai suru). The ta is "other"; the kai, "world." One is simply passing from this world, この世 (konoyo), to that, あの世 (anoyo). The English phrase "passing on" conveys this perfectly.
We all want 幸福な死に方をする (kō fuku na shinikata wo suru; to "die happy"), though this is not the same as saying, "I would happily die." I suppose that a natural death, or 自然死 (shizenshi), at a ripe old age is ideal.突然死 (totsuzenshi) is "sudden death," and few would look forward to that.