It would be nice to break it down by model if possible.
Apple has not released sales figures for their early systems, so your question cannot be answered accurately. I will therefore do so inaccurately. ; - )
Starting with that data and using tidbits from other (often conflicting) sources, I derived the following highly questionable figures which I've also shared in Google Docs.
Apple II 64,700
Apple II Plus 545,500
Apple //e 4,250,000
Apple //c 450,000
Apple //c Plus 200,000
Apple IIGS 979,000
The total is more than the Wikipedia estimate of between 5 - 6 million units. Some notes:
- The Apple II/II Plus figures were calculated from Reimer's totals by naively assuming a 50/50 split for 1979 and 1980. This doesn't affect the combined totals, but gets the II total close to the highest serial found (see the Google Doc). Note that there is a well-known A2S1 serial number jump from the early 40,000s to the 60,000s.
- BYTE magazine states the II Plus sold 500,000 units, though 750,000 is given elsewhere.
- A few morsels of //e sales data were provided by the always excellent Digital Antiquarian.
- The //c and //c Plus figures are perhaps the largest unknown. It's not clear if Reimer's data includes these systems. In particular 1990 and 1991 show no evidence of the //c Plus exit, so I've included them separately.
- Some sources say the //c sold 400,000 in its first year, whereas the Digital Antiquarian states it "averaged just 100,000 sales per year over its four years". This matches the tone of the book "West of Eden: The End of Innocence at Apple Computer" which chronicles that in summer 1984 "Panic was building over the IIc's performance ... it was dead in the water".
- I have no data on //c Plus sales so I've naively assumed it sold the same yearly as the //c.
- The IIGS data comes from Brutal Deluxe's Apple IIgs Serial Number project. Although their estimated total is 2.8 million, a former manager of the Apple II division has stated categorically that no more than 1 million were sold. Their data is useful for a rough sales per year pattern if scaled down to total no more than 1 million - which I have done. The yearly values have also been rounded down. Although the figures aren't accurate, they confirm the next point:
- The IIGS is almost certainly not included in Reimer's data, as the estimated IIGS sales for 1988 exceed Reimer's total for that year.
- You didn't ask, but "Two hundred Apple-1 computers were manufactured, and all except twenty-five of them sold over a period of ten months." Only 66 are known to still exist.
- Again not really relevant, but Apple III and III Plus sales estimates vary from 65,000 to "85,000 units by April 1984". (The latter source is probably more credible.)
- Reimer's figures obviously do not include the Apple IIe Card because it was sold until 1995.
- An important corollary is that according to my collated data, the Apple II line propped up Apple during the the first 4 years of the Mac era from 1984-1987. Mac sales finally eclipsed Apple II sales in 1988 (not 1987 as suggested by Reimer's data).
- Supporting the total of more than 6 million units, another answer linked to this 1990 video where Apple CEO John Scully states that "the Apple II has [...] about 6 million in the installed base today."
An attempt is being made by Antoine at Brutal Deluxe Software to estimate IIgs production figures based on serial numbers.
This work is using the fact that the serial number encodes the machine's position within a week's production run at a particular factory. Decode for each factory and week, look for the maximum value reported and you have a method of estimating total production over the product's life cycle.
Antoine is trying to cross-reference this with IIgs keyboard serial numbers (as the computers shipped with a keyboard), but the figures derived from IIgs vs keyboard serial numbers are currently (May '16) way out of sync (~2.6M IIgs's, ~0.9M keyboards).
The ~2.6M figure seems higher than other estimates.
I don't believe Apple ever released definitive numbers of all Apple II's sold, let alone by model.
I came across a primary source for this which doesn't provide a breakdown by model, but backs up the estimate provided by Nick's answer of over 6 million units, and could hardly come from a more authoritative source: the mouth of Apple CEO John Scully. The full video can be found here or here. At about 3:23 John says:
No the Apple II has been an extremely successful product. There is about 6 million in the install base today.
This video was dated 1990 in the credits, and mentions the 1990-1991 school year in the future tense, suggesting it was made between January and September 1990. Apple sold stopped selling its last Apple II model in November of 1993. Given the decline of the Apple II in favour of the Macintosh and many other competing companies gaining market share in the late 80s and the early 90s it's entirely plausible that the final total number of units sold remained between 6 and 7 million. It's also worth noting that 1990 is also the year according to Nick's estimates in which total sales would have exceeded 6 million lending some additional credibility to Reimer's estimates.
Your Apple ][ production number is low, mine is first half of 1979 production and is A2S1-22365. I have seen A2S1 serials as high as 65,515, with a mid (week 20) 1980 production motherboard.
Apple continued to sell the Apple ][ while making the plus, they didn't stop ][ production until early 1981.
Highest A2S2 serial number I've found A2S2-588366, week 5 1983 production (that's after the introduction of the //e in January, 1983), and that doesn't include A2S3 systems (Belll & Howell ][plus).
My Apple ][ is SN 66XXX dated week 23 of 1980. I agree with Howard Poe that there were a lot more Apple ][ computers produced than 20,000. If there were only 20,000 produced the price for one would be astronomical but they can still be purchased for a somewhat reasonable price. The release of the Apple ][+ in 1979 was not accompanied by an immediate cutoff of Apple ][ production as the Apple // production timeline graphics would have you believe. So I would definitely revise Nick Westgate's Apple ][ production number, but I think his other guestimates are reasonable, given the limited production data that is available.
numbers on Apple IIs - Low
numbers on Apple IIe - High
numbers on Apple IIgs - probably a little Low
numbers on Apple IIc+ - Way too high
I could be wrong, but this is based on working for an educational dealer for 10 years, over 40 years dealing with them and other sources.
By 1982 before the Apple IIe was made, they had sold 3/4 million Apple IIs and exceeded a million in June of 1983, not much after IIe intro.
Most estimates put the IIgs toward or over the 1 1/4 million units of both the Rom 1 (256K) and Rom 3 (1 meg) machines.
IIc+ wasn't introduced until late 1988 and had shortest run of any of the Apple II line. It was very unpopular, at the end of the Apple II cycle and not adopted by anyone other than home users. So, the IIc was probably higher and IIc+ was definitely lower, more likely less than 100,000 and probably closer to 50,000.