In "There Will Come Soft Rains," what literary device does Bradbury use most when he relates to the house?

I agree with mrs-campbell and would like to expand upon her answer a bit more.  I must say that after scouring the story, I could find no new examples of personification because she mentioned them all (and even included a couple that weren't exactly personification).  However, just because they are mentioned, doesn't mean they are explained.  My answer will explain how each example is an example of the literary element of personification.

First, when the stove "gave a hissing sigh."  This specifically refers to the house as a person.  A stove cannot make the sound of a sigh, only a person can.  And that sign often can mean boredom or resentment, but definitely something negative (and nothing good).

Second, the house mechanics are focused upon when the "tapes glided under electric eyes."  Note that it is a human that has eyes, nothing else does.  Giving mechanization such human qualities gives an ominous quality to the house and its contents, as if they were alive.

[Next, I have to say that, in my opinion, the third example (even though it is a great example of sound and touch imagery) is not an example of personification.  "Chimed" and "lifted" are not human, but mechanical qualities, so I must go on to the fourth to continue discussion.]

Fourth, the water goes down "a metal throat which digested it."  No doubt that it is only a human (or an animal) that has a "throat," therefore even though that is not a "quality" per se, it is actually a body part!  This is definitely personification here!

Further, shutting the doors and the windows tightly showed "old-maidenly preoccupation with self ... mechanical paranoia."  Yes, both "preoccupation with self" and "paranoia" are human qualities that actually prove to be quite advanced of thought.  Further, any concept of "self" is inherently human.

[Again, I have to disagree with the sixth example being personification specifically of the house.  It is personification of the mice, but yes, they are "angry" as only a human could be "angry."  Mice simply react out of instinct.  So in that case it IS personification, just not that of the house.]

Finally, "the house began to die."  Only living things can die and, although not innately human (but also relating to plants and animals) this could be considered personification as well.

Therefore, due to at least five of the above examples being perfect representations of personification, I must agree that personification is the most used literary element pertaining to the house.