To me, a race becomes "main" when it joins the standard tropes of Star Trek. The Andorians, for example, have been universally known among Trek fans since TOS, and (aside from their brief ban from TNG-era materials) have made consistent appearances in ancillary products. The Tellarites, on the other hand, nearly disappeared until ENT revived them and made them far more recognizable to the average Trek fan.
Using that criteria (species in parenthesis are part of the standard tropes of their series; those with asterisks are borderline as general cases – while someone might know them as, e.g. "Neelix's species" they wouldn't recall the race's name; italics indicate non-trope level development on a previous series):
TOS
Romulan
Talosian
Orion
Gorn
Horta
Klingon
Andorian
Tholian
TNG
Betazoid
Q
Ferengi
Bolian
Borg
DS9
Bajoran
Changeling
Trill
Cardassian
Vorta
Jem'Hadar
Breen
VOY
(Ocampa)
(Talaxian)*
(Kazon)
(Vidiian)
Species 8472
(Hirogen)
ENT
(Suliban)
(Denobulan)*
Tellarite
(Xindi)