I have done extensive research on this subject, looking up references in the original Greek and Latin sources. The Watchtower claim is not only erroneous, but it is also disingenuous.
1) The Romans did crucify prisoners and slaves in the first century with a two-beamed cross and the words crux and stauros did denote such an execution instrument (cf. Plautus, Lucian, Artemidorus, Seneca, Tacitus). The Society's repeated claim (1950 NWT, 6/22/1984 Awake!, 1984 Reference NWT) that Livy used crux to only denote impalement is totally without merit; I looked up every time Livy mentioned crux and he never was specific the way the Society claims he was. The claim (cf. 1950 NWT, 1984 Reference Edition) that Lucian used anastaroo to denote impalement in his play on Prometheus is also false; Lucian actually indicated a two-beamed cross. The Jewish historian Josephus described the Romans crucifying the Jews "in different postures" when they attacked Jerusalem (Jewish War, 5,450-451). By claiming that crux and stauros did not mean "cross" until the third century, the Society is intentionally distorting and hiding the facts.
Here are some ancient Greek and Roman references to crucifixion (stipes is the Latin word for the upright pole and patibulum is the word for the crossbeam):
"Being crucified is auspicious for all seafarers. For the stauros, like a ship, is made of wood and nails, and the ship's mast resembles a stauros." (Artemidorus, Oneirocritica, 2:53)
"Men weep and bewail their lot, and curse Cadmus with many curses for introducing Tau into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up the erections on which men are crucified. Stauros the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but supplied by his own shape--that shape which he gave to the gibbet named stauros after him by men." (Lucian, Trial in the Court of Vowels, 12)
"Suppose we crucify [anestaurosthai] him half way up somewhere hereabouts over the ravine, with his hands out-stretched from crag to crag....Do you suppose there is not room on the Caucasus to peg out a couple of us? Come, your right hand! Clamp it down, Hephaestus, and in with the nails; bring down the hammer with a will. Now the left; make sure work of that too." (Lucian, Prometheus, 1-2)
I suspect you're doomed to die outside the gate, in that position: Hands spread out and nailed to the patibulum....Oh, I bet the executioners will have you looking like a human sieve, the way they'll prod you full of holes as they run you down the streets with your arms on a patibulum, once the old man gets back! .... I'll give two hundred pounds to the first man to charge my crux and take it ? on condition his legs and arms are double-nailed, that is....I shall bear the patibulum through the city; then I shall be nailed to the crux." (Plautus, Miles Gloriosus, 359-360; Mostellaria, 55-57, 359-360; Carbonaria, fragment 2; Plautus wrote about 250 BC)
"Though they strive to release themselves from their crosses (crucibus)---those crosses to which each one of you nails himself with his own hand--yet they, when brought to punishment hang each one on a single stipes; but these others who bring upon themselves their own punishment are stretched upon as many crosses as they had desires. Yet they are slanderous and witty in heaping insult on others. I might believe that they were free to do so, did not some of them spit upon spectators from their own patibulum!" (Seneca, De Vita Beata, 19,3)
"I should deem him most despicable had he wished to live up to the very time of crucifixion (ad crucem). . . .Is it worth while to weigh down upon one's own wound, and hang impaled upon a patibulum? . . . . Can any man be found willing to be fastened to the accursed tree (infelix lignum), long sickly, already deformed, swelling with ugly tumours on chest and shoulders, and draw the breath of life amid long drawn-out agony? I think he would have many excuses for dying even before mounting the crux!" (Seneca, Epistle 101,10-14)
2) The Gospel accounts assume a two-beamed cross, especially in the motif of Jesus or Simon of Cyrene carrying the cross on the way to Golgotha (cf. John 19:17) which is nothing other than the widely-attested practice of patibulum-bearing (the patibulum was the crossbeam). This practice pre-existed the invention of crucifixion as a method to torture disobediant slaves (cf. Dionysius of Halicarnassus, Plutarch) and was widely adopted as a prelude to crucifixion (cf. Plautus, Plutarch, Artemidorus, Chariton). The Society would instead require Jesus or Simon to carry a pole to Golgotha (actually pictured in the Greatest Man Who Ever Lived book (1991, chapter 124), which is utterly without any historical support and ignores the copious evidence of patibulum-bearing. The traditional Christian picture of Jesus carrying the whole cross over one of his shoulders (seen in the Passion of the Christ movie) is also unhistorical....what the Romans did was have the prisoner stretch out his hands, nail or tie the hands to the crossbeam, and then having him bear the beam over his back or chest to the stationary stipes (vertical beam), and then hoist him up to the cross. This practice is also possibly alluded to in John 21:18-19 which also assumes a two-beamed cross. Details in John 20:25 and Matthew 27:37 are also best explained by assuming a two-beamed cross.
3) The use of the word xylon "tree, wood" in Acts 5:30; 10:39; 13:29, Galatians 3:13, and 1 Peter 2:24 does not indicate the kind of stauros Jesus died on, only that the Bible writers understood Roman crucifixion in terms of the law in Deuteronomy 21:23-23. Other Jewish writers referred to Roman crosses in exactly the same manner (including the Dead Sea Scrolls, Philo, Josephus), and Roman writers also referred to Roman crosses metaphorically as "trees" (cf. Seneca, quoted above).
4) There was a strong tradition in late first century and second century Christianity that repeatedly looked for prophecies and prefigurings of the two-beamed cross of Jesus in the OT, and described the stretching out of the hands from side to side as a sign of Jesus' cross (cf. Barnabas, Justin Martyr, Odes of Solomon, Irenaeus, Tertullian, etc.). Even the pagan Romans, in mocking the Christians, depicted a two-beamed cross (cf. the Palatine graffito).
There is lots more evidence, but this covers the basics.