The rock from which we were hewn (Baptists and Anabaptists)

 Baptist churches first emerged in the English-speaking world around 1609 (General Baptists), and 1640 (Particular Baptists) respectively.

The Particular Baptists are so called not because of some inate "pickiness" but because of their (our) belief, along with most other reformed Christians at the time, in Christ's particular redemption. The saving work of Christ on the cross and in the resurrection actually saved particular people. This is sometimes referred to as "limited atonement".  

The Particular Baptist churches in the English-speaking world emerged from existing independent congregations, which had sprung up in England from the late 16th century onwards. What made them "Baptist" was their conviction that baptism should be administered on profession of faith, and therefore should not be given to infants too young to profess faith. The practice of delaying baptism until the serious commitment could be made in an informed way was certainly a common practice as late as the fourth century, and many church fathers of that time, such as Basil of Caesarea or Gregory of Nazianzus, were baptised at a mature age, although they had been raised in Christian families. 

In the late 1630s and early 1640s the first Particular Baptist churches emerged in the London area. By 1644 there were seven of them in London, and together they formulated their beliefs (the First London Confession of Faith). What they wrote down is recognisably the same as what Baptists believe today. 

One question, however, which has been somewhat overlooked, is the influence of an earlier movement outside the English-speaking world, namely the Anabaptists, or, more specifically, the Mennonites in the Netherlands.

It was contact with Mennonites in Amsterdam which had convinced the General Baptists of the necessity of baptism on profession of faith around the year 1609. John Smyth was the first to embrace this new conviction, baptising himself. His second-in-command Thomas Helwys, was the one who ended up leading this congregation, and he returned to London in 1611 to continue his ministry in his homeland. 

Likewise, there was contact between the Particular Baptists and Mennonites. A certain Richard Blunt was sent to the Netherlands around 1640 to be baptised by Mennonites, and to learn the technique of baptism by full immersion (up to that point Baptists baptised by other modes such as pouring or sprinkling). It is my understanding that following this contact, baptised churches in England continued to consider the continental Mennonites their brethren, notwithstanding differences in language, soteriology, and interaction with the "world".