Recently released new Halo materials have now called into question just how many Spartan-III's there are/were. Our original understanding is such: Alpha and Beta Companies each had more than 400 candidates, and exactly 300 graduated as Spartan-III's. All 300 of Alpha and all but 2 of Beta were killed in Operation: PROMETHEUS and Operation: TORPEDO respectively. All of the 330 of the Gamma candidates became Spartans, and except for those involved in the Battle of Onyx, their status is unknown. That means a total of 930 Spartan-IIIs. Halo: Reach and Headhunters have complicated this.
I'll start with Halo: Reach. Save for Jorge, all the members of Noble Team are Spartan-IIIs from Alpha and Beta. We know that Kurt and Mendez were able to avoid handing a few of their soldiers over to Ackerson to be sent on a suicide mission. So in Alpha Class were there 300 Spartans, plus Carter, Emile and Jun? Or are they included in the three hundred, and as such fewer than 300 were actually sent on PROMETHEUS. The same goes with Beta, Noble Six and Catherine, and TORPEDO.
The Headhunter program further complicates things. We don't know which class they were drawn from; it could have been any or all of them. However we do know that at the progam's height there was a maximum contingent of six squads (pairs) with a total of seventeen soldiers in to fill gaps when half or all of a team was lost in the field. Halo: Evolutions states that they were taken from the Spartan-III program but fails to stipulate whether this was before or after their "graduation" as full Spartans.
So which do I think is most likely? Well, I find it very hard to believe that a man as meticulous as Ackerson would fail to notice that he was supplied with even one fewer than the 300 Spartan-III's he was promised for PROMETHEUS or TORPEDO. Ghosts of Onyx is also very clear that there were exactly 300 Spartan-IIIs deployed at both these battles. It therefore seems far more likely that on both occasions Kurt and Mendez trained 300 Spartans, plus a few extras they didn't tell Ackerson about, and didn't hand over to him. The language of this memo seems to support this view.
As for the Headhunters? Really either could be true. Once again we know that 300 Spartans fought in Prometheus and Torpedo; therefore the headhunters being part of the 300 is unlikely because we know that at least four, and almost certainly more, were killed in Headhunter missions. Thus this would leave a shortfall. So if the Headhunters were taken from Alpha or Beta Companies, they were almost certainly separated during training and there were 300 regulars + the Headhunters. However if they came from Gamma company they would have to be part of the class 330, because every candidate "graduated." There would be noone else to recruit. Coming from Gamma is problematic however because they were just about to graduate at the time of the Battle of Onyx; there likely wouldn't have been time to launch a series of headhunter operations before that happened.
So in conclusion what is the most likely scenario for the number of Spartan-IIIs? In my opinion: 300(Alpha Company) + 3(Carter, Emile, & Jun) + 300(Beta Company) + 2(Noble Six & Catherine) + 330(Gamma Company) + (Thom-A293) + (17 or more Headhunters) = 953 or more Spartan-IIIs. There may even be a few more Spartans that Kurt and Mendez were able to sneak out of the program.