Actually, the one allegedly formed by Lane's Brigade at Gettysburg on July 1, 1863 was just that--alleged. There is a single source that claims that it happened--Capt. Eminel P. Halstead, of Doubleday's staff. In a post-war MOLLUS paper, Halstead claimed that Lane's Brigade formed square in response to a feinted charge by Gamble's and Devin's brigades late in the afternoon on July 1.
The problem is that Halstead's account is the ONLY one that makes this claim. Winfield Scott Hancock, atop East Cemetery Hill, described Buford's troopers, drawn up in line of battle, as standing "unshaken and undaunted," but made no reference to a square. No contemporary account says anything about Lane forming square. Not one. Buford didn't mention it in his report, nor did Gamble or Devin.
O.O. Howard sent Halstead to Buford with orders to do something to halt the Confederate advance. Buford, operating on the flank, supposedly rose in his stirrups, pointed at the massed Confederate infantry, and asked, "What in hell and damnation am I supposed to do?" Halstead said, "I don't know, General, but those are General Howard's orders."
Buford ordered the two brigades to deploy into line of battle, sent men forward to tear down fences to clear the way, and visibly made ready to make the charge with bugles blowing. The charge itself was never ordered by Buford. It was not necessary.
Having said that, something halted Lane's advance that day. It was probably the sight of two full brigades of cavalry--roughly 4000 troopers--mounted, in line of battle, with sabers drawn, awaiting the order to charge. But there is no evidence that Lane actually gave the order to form squares by echelon, and there is no evidence that they actually did so.
The feint was enough. Lane's advance halted, which allowed time for the Union infantry to fall back safely from its very exposed position on Seminary Ridge to the positions that Hancock and G. K. Warren had prepared on East Cemetery Hill.
What gets lost in the shuffle is that the 52nd North Carolina Infantry of Pettigrew's brigade DID, indeed, form square that day. Col. James K. Marshall was advancing on the end of Chapman Biddle's line on McPherson's Ridge, and was about to overlap it.
Troopers of the 8th Illinois Cavalry, posted to the left of the Union infantry, spotted this advance, realized that Biddle could not see the Confederate infantry due to its being hidden in a swale, and made noisy preparations to charge, including bugle calls, etc. Marshall ordered his regiment to halt and form square the receive the charge, which never came. However, Biddle spotted the movement and ordered his men to fall back to Seminary Ridge, which they did safely.
This episode--notably missing from your list--is well documented. It appears in the entry for the 52nd North Carolina in Walter Clark's compilation regarding North Carolina troops in the war. Marshall was killed during Pickett's Charge, so he left no report, but I have no doubt that he would have mentioned it.
In case it's not clear from this post, I first began researching this episode in 1992 and continue to search for sources about it. I am quite confident that the 55th North Carolina formed square on July 1. The veterans corroborate that.
Lane's brigade, not so much. There are no other accounts--on either side--to corroborate Halstead's claim. As said above, SOMETHING halted the Confederate advance, and it was undoubtedly the sight of Buford's two brigades drawn up, ready to charge. But there simply is no proof to corroborate Halstead's claim.
Most notably, there are no claims that the Confederates formed square when the 5th U.S. Cavalry charged Hood's infantry at Gaine's Mill in May 1862, or when the 1st Pennsylvania Cavalry charged Jackson's infantry at Cedar Mountain on August 9, 1862. Both charges failed miserably, although the charge of the 5th U.S. at Gaine's Mill did appear to halt the Confederate momentum and halted the rout of the 5th Corps.
Similarly, there are no claims that the Confederates formed square to repulse Farnsworth's Charge at Gettysburg on July 3. Perhaps they realized that a cavalry charge uphill, into the teeth of two batteries of artillery, was destined to fail miserably and that they didn't feel that they needed to do so.
UPDATE, 10:30 PM: I have put together a lengthy blog post that addresses this issue in great detail, and which includes a rare image of a Union infantry regiment drawn up in a hollow square, on my blog. The post can be found here: http://civilwarcavalry.com/?p=3578