A needle is, as Doug Henning used to note in performance, the natural enemy of the balloon. Thus, it is not surprising that the effect of penetrating a needle or spike through a balloon has been approached many times. One early entry was William G. Strickland's “The Pneumatic Pincushion,” in the March 1930 Magic Wand, Vol. 18 No. 145, p. 73. That effect, as with other versions, began with having the balloon inserted into a box, which was then pierced with several knitting needles, with no harm to the balloon. Subsequent versions also used some sort of covering box or tube. Several of these were marketed.
The effect of piercing a fully unconcealed balloon—what we now think of as the “Needle Through Balloon”—was devised by Tom Ransom, and published in the New Phoenix of July 23, 1954, No. 312, p. 51 as “No Bop Balloon”. In this, a large hatpin was stuck into a balloon, and by doing this at the end of the balloon (where the rubber is thicker), the balloon would not burst.
In England, in February 1956, Roy Baker marketed the “Pincushion Balloon”; see the Feb. 4, 1956, issue of Abracadabra, Vol. 21 No. 523, inside front page. This was essentially the Ransom method, but Baker had discovered a balloon that was manufactured with more than one thick spot, so that it could be pierced by needles at several places without bursting. The British celebrity-magician David Nixon performed this on his television series in 1956. In the December 1956 issue of The Gen, Vol. 12 No. 8, p. 172, this was described by Harry Stanley, who stated that it was the Ransom method (albeit without mentioning Ransom by name—starting a sad tradition in regard to this trick).
In the March 1957 issue of The Gen, Vol. 12 No. 1, p. 278, appeared “Supertration” by G. N. Rhodes, wherein a balloon was pierced by several hatpins. This made use of pieces of transparent tape placed in spots on the surface of the inflated balloon. The tape prevented pins from bursting the balloon, which produced the same effect as Baker's “Pincushion Balloon”. However, the tape, although transparent, could be seen, so Rhodes covered the balloon with a hairnet to camouflage the tape patches.
Across the ocean, U. F. Grant had made the same discovery as Rhodes, but put it to a different use. In April 1957, Grant's “Bowl Fountain” was published in Hugard's Magic Monthly, Vol. 14 No. 11, p. 557. A tape-prepared balloon, filled with water, was concealed in a bowl and, when punctured, produced a thin waterspout.
In his 1959 booklet T.V.'s Original Balloonatic (p. 16), Dwight Damon published the idea of running a single strip of transparent tape over the length of a balloon. This seems to have beat the visibility problem. At least, Damon doesn't mention it. Perhaps he kept the strip of tape turned to the top surface of the balloon and out of direct view.
The following year, U. F. Grant applied the tape method to the Pincushion Balloon effect, but had to surmount the same problem that Rhodes faced: the visibility of the tape. Instead of a hairnet, Grant used a sheet of tissue paper in a clever way. See “Grant's Pin Cushion Balloon” in Balloon Side Show, 1960, p. 14.
From there, the effect using the tape method with ordinary pins appeared in various beginner's books.
In the June 1962 Linking Ring, Vol. 42 No. 6, p. 65, Bernard J. McGory, Jr. had a piece called “Heart Surgery,” in which a red balloon was pierced using a large threaded upholstering needle. The balloon was “sewn” with the curved needle, meaning that the penetration went from outside in and from inside out, with the thread pulled along the route. This used the tape method (McGory correctly credits Rhodes, and mentions Grant).
In 1974, the German magic dealer Borretti marketed “Super Needled Balloon” which was advertised in English-language magic magazines by the start of 1976 (see The Linking Ring, Vol. 56 No. 1, Jan. 1976, p. 147). This used the Ransom-Baker method and a transparent balloon (not a new idea) and a very large and sharp metal needle. The only new technical feature was the advice to lubricate the needle, making it less likely that such a large skewer would snag and burst the balloon.
In December 1977, on his second NBC special, Doug Henning performed the Needle Through Balloon using the oversized needle and transparent balloon. Almost overnight, it seemed that every dealer was selling those large needles along with the same type of colorless balloon that had been used by Henning. Thus, the Ransom-Baker method became hugely popular, and continues to be so today. Amusingly, when Henning did it on his TV special he used the tape method.
Much of this information has been drawn from Max Maven's article, “Tracking Slum Magic to Its Lair: The Needle Through Balloon” in the Winter 2014 issue of Gibecière, No. 9 No. 1, p. 87, where further information can be found.