In my opinion, one of the passages that most clearly support the belief that the dead are unconscious is Psalm 146:3-4:
3 Trust not in princes -- in a son of man, For he hath no deliverance. 4 His spirit goeth forth, he returneth to his earth, In that day have his thoughts perished. [YLT]
3 Put not your trust in princes, nor in the son of man, in whom there is no help. 4 His breath goeth forth, he returneth to his earth; in that very day his thoughts perish. [KJV]
This is one of several passages that are commonly cited by adherents of the doctrine of Christian Mortalism (also more colloquially known as the doctrine of "Soul Sleep"). Other similar passages (courtesy of this answer) are Genesis 3:19, Ecclesiastes 9:5, Ecclesiastes 9:10, Ecclesiastes 12:7, Psalm 6:5, Psalm 88:10-12, Psalm 115:17 and Isaiah 38:18-19.
The same aforementioned answer concludes:
Do these scriptures make it seem as though the dead are capable of speaking, thinking, or being aware? Death is said to be silent and as the darkness. It's called the land of forgetfulness. The dead cannot thank, cannot praise, cannot hope; all feats that require mental faculties to be accomplished. In Sheol, there is absolutely no declaration of God, or of His faithfulness/graciousness, or of anything He performs. When we die, our spirits depart to God who gave it, and we return to the dust from which we were taken; consequently, our thoughts perish altogether. And most of all, the dead know naught; they have no knowledge, wisdom, thinking, or work in the place where they are.
Question: Does Psalm 146:3-4 affirm that the dead are unconscious? To what extent is a different interpretation warranted?
Related questions:
Does Ecclesiastes 9:10 affirm that the dead are unconscious?
Are the souls of Revelation 6:9-11 awake and, yet, still awaiting the resurrection?
Does "asleep" in 1 Corinthians 15 mean that the dead are unconscious prior to the resurrection?
The dead forget OR the dead will be forgotten? Ecclesiastes 9:5