I assume the tens of billions, at least.
Seems a fair guess, given how long they’ve been at it and how much territory they eventually cover: http://memory-alpha.wikia.com/wiki/Borg_history
How many? Lots and lots! Resistance is futile. 
IIRC the highest Borg designation we ever hear in the TV shows is just over 10,000 so let’s call it 10,000 as a round number (also, there is more Star Trek after this and the Borg keep going but have to pick a date somewhere. I assume the Borg number each new species sequentially and not randomly (sequentially is more efficient and thus Borg-like).
As to how many the Borg assimilate each time is highly variable and not every species is successfully assimilated (such as humans or Klingons). In some cases a few hundred thousand. In others millions. If they assimilated earth one would suppose they’d nab a few hundred million (the rest dying fighting).
So, as a WAG, call it 10 million on average. That would mean they have assimilated 100 billion individuals.
That is a super soft guess though. Too many variables we do not know for a very good guess.
Are we counting Borg-born babies that receive their implants and nanites in infancy? There are probably a lot more of those than adult assimilations.
They used to not assimilate anyone. They raised Borg Babies in drawers. They ignored you if you walked around inside their ships. They didn’t care about others much at all.
And there used to be just one cube. Because, why would there be any more?
Damn you Sweden!!!
I’ve always wondered about the Swedish Chef; you can’t see his eyes.
This would be my guess.
Your estimate matches SyFy’s. Species 8472 killed tens of billions of Borg, so that has to be the lower boundary.
There are a few additional notable comic-book examples deserving of being on that list, in addition to Thanos and Krona. Marvel’s Beyonder wiped an entire galaxy in the first issue of Secret Wars just to show he meant business (and was on the verge of wiping out everything when he was finally stopped), and DC’s Mister Mxyzptlk and Bat-Mite destroyed the entire DC multiverse, though they fixed it afterward because apparently it’s a regular thing they do (Superman and Batman: World’s Funnest).
Yep, they were not about assimilating at all. They were tech geeks that just wanted everyone’s technology.
Then one day they were chasing the Enterprise to add the tech to their own, when the ship suddenly vanished. Not knowing that it was Q that sent it away, the Borg decided that humans were just that damn impressive, and needed to be brought into the collective.
That’s why the Borg were awesome on TNG. Then the writers forgot everything that made the Borg interesting, and they were simply wasted on Voyager.
And on Voyager, the Borg didn’t know noth’n about raising no Borg babies. (Ref. “Drone”)
In the show, it was easy to imagine humans getting assimilated because they were the same size and shape but could/did they assimilate other bigger or odd shaped beings?
Well, they tried to assimilate the Omega molecule and got their asses kicked.
And they tried to assimilate species 8472 and also got their asses kicked.
I get the impression they should stick to assimilating humanoids.