Pretty much all hunting rifles that I have ever seen are bolt action. I would venture to guess that those are more prevalent, but I would welcome statistics.
For small calibers, semi-auto is fairly popular (specifically, Ruger), though I'm sure sure of stats.
For .30 caliber, there's little point, since there is added cost, potential reduction in velocity (enough to matter?), but no added utility, and common bolt actions are crazy simple, which helps keep them reliable, safe, and potentially easier to clean in the field
(Browning-revised level-actions likely have similar advantages, and have also remained fairly popular, especially throughout the Americas). They can also be made lighter than most other action types, for a given cartridge and barrel length. Firing rate isn't all that important. People do hunt with semi-autos, but I think refinements on ~1900 bolt designs will outlast all of posting in this thread.