What is the basis of the Jehovah's Witnesses' belief that Jesus died on a Stake instead of a Cross? I understand that the Jehovah's Witnesses teach that Jesus died on a Stake (a vertical pole) instead of a Cross.    What is the basis—biblical or other—for this belief?  Does history and archaeology show that the Roman form of crucifixion used just a vertical pole instead of a cross?  Was this unique to Jesus' death alone?
The Jehovah's Witnesses have addresses this issue. From their web site:
https://www.jw.org/en/bible-teachings/questions/did-jesus-die-on-cross/


  Many view the cross as the most common symbol of Christianity.
  However, the Bible does not describe the instrument of Jesus’ death,
  so no one can know its shape with absolute certainty. Still, the Bible
  provides evidence that Jesus died, not on a cross, but on an upright
  stake.
  
  The Bible generally uses the Greek word stau·ros′ when referring to
  the instrument of Jesus’ execution. (Matthew 27:40; John
  19:17) Although translations often render this word “cross,” many
  scholars agree that its basic meaning is actually “upright stake.” *
  According to A Critical Lexicon and Concordance to the English and
  Greek New Testament, stau·ros′ “never means two pieces of wood
  joining each other at any angle.”
  
  The Bible also uses the Greek word xy′lon as a synonym for
  stau·ros′. (Acts 5:30; 1 Peter 2:24) This word means “wood,” “timber,” “stake,” or “tree.” * The Companion Bible thus
  concludes: “There is nothing in the Greek of the N[ew] T[estament]
  even to imply two pieces of timber.”