I've seen a couple of references to Kepler saying "Between Jupiter and Mars I put a planet", but he actually wrote that this was a failed attempt which included a planet between Mercury and Venus as well. Later, he came up with his nested polyhedrons defining the possible planetary orbits, making the asteroids and Uranus impossible. [Hoskin]
Numerology is more like it. Yes, it predicts a planet where the asteroids are, and it predicted Uranus. But, looked at closely, it fails to predict Mercury. [Mehlman1]
No families yet, but with Piazzi's discovery of Ceres we have an orbit that's more than speculation. The subsequent discovery of Pallas by Olbers was a surprise, but after that more were expected. [Serio]
Gauss's method of calculating orbits from only a few observations began with his work on the orbit of Ceres. [Weiss]
Daniel Kirkwood's first major "discovery" was a discredited and forgotten theory about the rotation periods of the planets. His finding, from a study of the orbits of fewer than a hundred asteroids, of missing orbits where the period was a simple fraction of that of Jupiter was a major success. [Fernie] [Mehlman2]
Kiyotsugu Hirayama noticed that many asteroid orbits were more similar to one another than chance would allow. He originated the modern concept of asteroid families, which are now sometimes called "Hirayama Families". [Schilling]
Max Wolf discovered the first Trojan asteroid, Achilles, in 1906 and more followed. They orbit the sun in lockstep with Jupiter, in orbits first shown to be stable by Lagrange in 1772. Later, asteroids with similar orbits related to other planets came to be called trojans as well but with their planet named. [Schombert]
Bode's Law and the Discovery of Ceres Michael Hoskin
American Scientist Online J. Donald Fernie
"Bode's" "Law" Bruce R. Mehlman
Kirkwood Bruce R. Mehlman
All in the Asteroid Family Govert Schilling
Trojan Planets James Schombert
Giuseppe
Piazzi and the Discovery of Ceres Foderà Serio et al
(In pdf format, requires
Adobe Acrobat or equivalent)
Gauss and Ceres Leorah Weiss