Star Trek TNG's Data was an andriod created by Noonien Soong, who was the Albert Einstein of robots. He was a busy guy and I think I can count about 4 total robots.
Does anyone know all of the Data-style robots that were mentioned in the series?
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It's quite amazing how many different numbers we have here, all attempting to address the same question. Some are more or less correct, some not at all, and some are correct within the scope defined by the answer but not the question.
This confusion seems to stem from the fairly wide variety in the natures and origins of all the Soong-type androids. In hopes of clearing this up, I'll try to cover this question from all angles.
I'm starting here, with the narrowest category. This includes only the androids built by Soong himself, which became fully functional, and are actually seen in Star Trek movies and TV series. This list includes the following:
Slightly narrower in some ways, yet broader than others, this category is meant to cover all androids which Star Trek viewers would easily recognize as being "Data-like".
This category includes only androids which actually have similar design and programming as Data. These androids have a few specific features that make them unique from the others.
This excludes Juliana Soong, because she was not programmed to be aware of her true nature and her identity was not really her own. Also, she looked nothing like Data.
This includes the prototypes prior to B4 because we can reasonably assume they were also physically modeled after Soong, and the fact that they were not fully functional excludes them from the other requirements.
This excludes Lal, because Data deliberately built her so that she could realize her identity, even including her species and gender appearance, on her own - it was not pre-programmed as with the others.
This list includes:
This is the most all-encompassing category of Soong-type androids. It covers all Soong-type androids created by Soong himself, which would include Data and all of his predecessors as well as Juliana Soong. This also includes Lal, who was later created by Data.
All of the lists above are based on information taken from Memory Alpha. Aside from those already linked, there is another article which is important - TNG Season 7, Episode 10: Inheritance. It is important, because it is in this episode that we discover that there were three prototypes created prior to Lore. (If you want to review the episode, the pertinent discussion takes place around 20 minutes in.) These three are not explicitly named in any episode or movie, but they would presumably include B-4. This is why some of the above lists include two unnamed prototypes. Unfortunately, we never canonically find out much else about these prototypes other than that they existed.
Seven or Eight, depending on definition.
From Memory-alpha on the nature of B-4
He was one of four failed prototypes before the construction of Lore was successful. (TNG: "Inheritance")
From Memory-alpha on Juliana Trainer
O'Donnell assisted Soong in his work on artificial lifeforms, and helped create the android Data, as well as his five predecessors, including Lore and B-4.
From this we can deduce that there are 7 Soong-type androids created by Dr Soong (Data + 5 predecessors + Juliana's copy), with Lal another Soong-type created by Data making it 8 in total.
Four. From Wikipedia:
Noonian Soong: Human cyberneticist who created Data, played by Brent Spiner, who also plays the role of Data. Soong has created four complete androids in the known Star Trek universe, Data, Lore, and B-4 (all three of the same design), and a replica of his dead wife Juliana, which is technically superior to his previous models. Early in Dr. Soong's career he was widely hailed as Earth's foremost robotic scientist, but he became a recluse after apparently failing to create a positronic brain and was thought to have been killed with other colonists on Omicron Theta. The scientist actually settled on Terlina III and summoned Data there to fit him with his final invention, an emotion chip. He inadvertently also summoned Data's brother, Lore, who killed him after obtaining the chip.
Noonien Soong built a total of six androids. 2 Unnamed prototypes, B4, Lore, Data and then Julianna Soong (copy).
Eight, Three prototypes that died, Lore, Data, his wife Juliana and Data's daughter Lal, made by him. This information is from the 1999 edition of the Star Trek encyclopedia. B-4 is the eighth, an unknown fourth prototype made. I believe that the first three prototypes are now with Starfleet robot research and the theft of one of these prototypes would be known by the Enterprise crew.