The answer to this question is not as straightforward as it first appears. If the question is asking specifically about "pilgrims," then the answer is 30. The narrator makes 1, and he meets 29 other travelers. That makes a total of 30 people with the specific intention of making the pilgrimage to Canterbury in order to visit the shrine of Saint Thomas Beckett.
Ready to start upon my pilgrimage
To Canterbury, full of devout courage,
There came at nightfall to that hostelry
Some nine and twenty in a company
But the group that travels to Canterbury is larger than only 30 travelers. The group also includes the host, Harry Bailey. Then, to be very specific, the group eventually picks up a character named the Canon's Yeoman. That takes the group total to 32.
Along the way, each member of the group is supposed to tell 2 stories. Those stories flush out each character more in depth, but Chaucer died before he could complete the work.
In the General Prologue of The Canterbury Tales, Chaucer the pilgrim describes a company of 29 pilgrims who arrive at the Tabard Inn. Chaucer writes:
Bifil that in that seson on a day,
In Southwerk at the Tabard as I lay
Redy to wenden on my pilgrymage
To Caunterbury with ful devout corage,
At nyght was come into that hostelrye
Wel nyne and twenty in a compaignye (ll. 19-24)
In other words, Chaucer the pilgrim explains that he was ready to ride on a pilgrimage to Canterbury when a company of 29 pilgrims arrive at the Inn. Chaucer the pilgrim joins the company as does the inn-keeper, also known as the Host or Harry Bailey.
Thus, there are 31 total pilgrims who make the journey to Canterbury.
29 pilgrims, and Chaucer, the narrator, makes 30. Chaucer died before he finished writing the stories all the pilgrims were to tell. The plan was one on the way and one on the way back. They were all to vote based on entertainment value and the moral taught--the winner gets a free dinner paid for by everyone else upon their return to the Tabard Inn.
Including Chaucer, 30, though not all tell tales.