There are guesstimates of their numbers ranging from as little as three all the way up to hundreds. Still other accounts say there were actually a thousand strong.
We know five were "killed" by Tuor, three by Ecthelion, and two score (40) by the warriors of the king's house. Combine those with the one disturbed in Moria in the TA, that makes at least 49 Balrogs.
Is there any other indication in Tolkien's works of a total number or mentions of any others?
Christopher Tolkien indicates that his father eventually decided there were no more than seven Balrogs.
"In the margin my father wrote: 'There should not be supposed more than say 3 or at most 7 ever existed.'"
But as you noticed, there are plenty of references in earlier writings to the existence of a great deal of Balrogs. Tolkien himself noted that in early writings, Balrogs were much more numerous and destructible than they later became.
Crucially, that note - which is invariably cited in any discussion of the number of Balrogs - was not necessarily Tolkien's final word. We really can't know for sure because Tolkien changed his mind, and we don't know if he changed his mind again.
So it's up to you - 7 or "a lot."
According to Christopher Tolkien's note at the start of "The Earliest Annals of Beleriand" (SoME, p. 351), this is likely a much later work (although precise dating of these manuscripts is impossible.) In this text, we find
There came afresh a hundred thousand Orcs and a thousand Balrogs.
In fact, there is only one marginal note (which @Shamshiel pointed out) that EVER suggests the number should be considered limited, while there are dozens of references to "armies," "hordes," and even "thousand(s)."
This preponderance of evidence leads me to argue that there we are fully justified in stating there were, at some point, thousands of Balrogs - although this number clearly had dropped significantly after Fionwe crossed Sirion in the War of Wrath, wherein
[t]he Balrogs were destroyed, save some few that fled and hid themselves in caverns inaccessible at the roots of the earth.
The number of Balrogs changed as Tolkien's conception of the world evolved, and we shouldn't take material from the Lost Tales or Quenta Noldorinwa too literally: in the Lost Tales Beren was an Elf and the precursor of Sauron was a big cat, after all.
In the earliest concepts Balrogs weren't even Maiar, after all, so if we accept the numbers of them from those writings, should we also accept the contradiction of them not being Maiar?
By the time of Lord of the Rings the concept had changed, and a Balrog was now a destructive force capable of wiping out the mightiest Dwarf kingdom.
The figure of "3, or at most 7" comes from the Balrogs that we definitely know existed:
A fourth, "Lungorthin, Lord of Balrogs", appears in the early Lay of the Children of Hurin, but there is some doubt over him (is it another name for Gothmog? is he just a Balrog lord?), and this work of course is more representative of the earlier concepts than the later.
There is, however, another named "Balrog" (not really a "Balrog", but the intention appears to be that we're talking about the same type of spirit, so I'll use "Balrog" as a convenient shorthand) in Tolkien's work who is rarely considered, but who survived to the end in all writings:
Arien the maiden was mightier than he, and she was chosen because she had not feared the heats of Laurelin, and was unhurt by them, being from the beginning a spirit of fire, whom Melkor had not deceived nor drawn to his service.
As always, remember that we're dealing with legends from a mythical age rather than a precise history here (Tolkien himself calls them "the mythology and legends of the Elder Days" in his foreword to LotR). Contradictory or confusing statements are to be expected.
TL;DR: It is not known.
There are different mentions of the numbers of Balrogs. Christopher Tolkien mentions that there were thousands or hundreds, whereas Tolkien himself only mentions seven.
The early conception of Balrogs makes them less terrible, and certainly more destructible, than they afterwards became: they existed in 'hundreds' (p. 170), and were slain by Tuor and the Gondothlim in large numbers: "thus five fell before Tuor's great axe Dramborleg, three before Ecthelion's sword, and two score were slain by the warriors of the king's house.
― The Book of Lost Tales Part Two, commentary by Christopher Tolkien on "The Fall of Gondolin"
There came wolves and serpents and there came Balrogs one thousand, and there came Glomund the Father of Dragons.
― The Lost Road and Other Writings, Quenta Silmarillion, Chapter 16, §15
In the margin my father wrote: 'There should not be supposed more than say 3 or at most 7 ever existed.'
― Morgoth's Ring, Section 2 (AAm*): note 50
The latter might be the most correct, since it's the only note from Tolkien himself
To ask these questions one has to take into account Tolkien's late ideas, not earlier, rejected ones. The texts that speak of hundreds of Balrogs and of Elves killing them by dozens in Gondolin are all very early texts, or texts that were never fully revised. At this time, Balrogs were still creations of Morgoth (and Gothmog was even his son). That's why in the published Silmarillion, Cristopher removed most of the references to hosts or thousands of Balrogs.
When Tolkien decided that Morgoth couldn't create life, he turned Balrogs into Maiar, and as consequence, he reduced their number greatly. That's why he said that only 3-7 ever existed. This note may not be definitive (it's possible that there were 10 or 20, instead of 7), but certainly his last intention was that there weren't a lot of Balrogs.
It's even possible that he wouldn't have made Glorfindel fight a Balrog if he had rewritten the tale of Gondolin. In one of Tolkien's last essays (found in History of Middle Earth vol. XII) he changed the name "Balrog" for "demon" when writing about this battle.
