The Stranger is indeed the death god of the Faith of the Seven as well as the god of the unknown. I imagine the main reason very few people pray to him is the taboo surrounding death that exists in most human cultures. Most people just don't like thinking about death, let alone praying to its personification. For similar reasons, the Stranger is the only god without hymns.
In addition to his unpleasant domain, the Stranger, in his name and his popular depictions, is seen as inhuman, distant, and unknowable. The statue of the Stranger that Stannis burns was "carved to look more animal than human" (CoK, Davos I). The Stranger's likeness in the Red Keep also has a "halfhuman face" (CoK, Sansa IV) Catelyn Stark's description of a sept's statue of the Stranger is particularly unappealing:
...the Stranger was neither male nor female, yet both, ever the outcast, the wanderer from far places, less and more than human, unknown and unknowable. Here the face was a black oval, a shadow with stars for eyes. It made Catelyn uneasy. She would get scant comfort there. (CoK, Catelyn III)
Basically, the Stranger is creepy. But there are actually a few instances of people praying to the Stranger in the books, for a series of reasons:
KINSHIP
Tyrion lights a candle to the Stranger in a sept:
Tyrion lingered after his cousin had slipped away. At the Warrior’s altar, he used one candle to light another. Watch over my brother, you bloody bastard, he’s one of yours. He lit a second candle to the Stranger, for himself. (CoK, Tyrion III)
Tyrion's prayer "for himself" is a bit ambiguous. If he was lighting a candle to prevent his death, it seems odd that he wouldn't light one for Jaime at that altar as well. My guess is that because the Stranger is the "outcast" according to Catelyn, Tyrion thinks he is also "one of" the Stranger's the way Jaime is "one of" the Warrior's.
Likewise, the Silent Sisters who prepare bodies for burial are considered servants of the Stranger, and presumably pray to him fairly often.
IN THANKS
Cersei gives another example of why someone might light a candle to the Stranger: to thank him for someone else's death.
One day she must light a candle to the Stranger for carrying Renly off and leaving Stannis. If it had been the other way around, her life would have been harder. (FfC, Cersei II)
FOR DEATH
Cersei implies in the same chapter that those who want death also pray to the Stranger.
"...When we find the Imp, we will find the Lady Sansa too. She is not dead... but before I am done with her, I promise you, she will be singing to the Stranger, begging for his kiss.” (FfC, Cersei II)
This is also the purpose of the statue of the Stranger in the House of the Many-Faced God, a place in Braavos fore those seeking death.
SHEER DESPERATION
Cersei prays to the Stranger when she is in great peril.
All the prayers they had taught her as a girl came back to Cersei... and she made up new ones as needed, calling on the Mother and the Maiden, on the Father and the Warrior, on the Crone and the Smith. She had even prayed to the Stranger. Any god in a storm. (DwD, Cersei I)
The fact that Cersei's prayer to the Stranger is remarked upon as unusual even though her life is at stake, indicates that people probably don't pray to the Stranger to prevent death. Indeed, when Stannis attacks King's Landing, Sansa notes that the brightest altars are the Warrior (god of warriors and combat) and the Mother (goddess of mercy).
EDIT: The wiki points out an interesting depiction of the Stranger in the newest Winds of Winter sample chapter I thought I'd add. Minor spoilers:
A Braavosi play called Bloody Hand depicts a fictionalized account of Tyrion Lannister. In the play, a psuedo-Tyrion meets with the Stranger and is implied to strike a sort of Faustian bargain. Mind you, the Braavosi are not the best source for Westerosi religious beliefs. But that seems to confirm that the Stranger is seen as the patron god for the outcasts of Westeros.
"Him of Many Faces." "And many names," the kindly man had said. "In Quohor he is the Black Goat, in Yi Ti the Lion of Night, in Westeros the Stranger." (FfC Cat)Though it's probably still true that he has more aspects than the stranger.