I don't own one because I own a 30-40 Ackley which for all intents and purposes is a 30-06.
The reason I own this rifle, which is built on a single-shot '98 Mauser action is because I inherited it from my father. Since I thinned the herd, as they say, I only own three rifles and one handgun. The 30-40AI works great on deer, elk, bear and moose which are what I hunt.
If something were to happen to the Mauser and I had to buy a new hunting rifle it would be a 30-06. I have owned a few '06 rifles in the past, my favorite was a '03 NRA Sporter with Lyman sights.
In reality I think that any of the cartridges in the '06 class perform pretty much the same on game. I doubt if any animal would know the difference if it were to be shot with a .270, .280, 7MM, .300 Mag or whatever. But there is also the aesthetic side of things. The .308 is an ugly little squat looking cartridge IMO. The '06 case is nicely designed and, well, handsome would be the word, I guess.
History means a lot to me and the older cartidges hold a certain fascination for me that goes beyond such mundane subjects as relative efficiency, 2" of difference in 300 yard trajectory and whether one cartridge kicks more than another. Personally I can tell little difference in the recoil of a .270, .308, 30-06 and 7mmRM.
I have a small block Chevy and I hate apple pie. 'A 30-06 is never a mistake' is a cliche for a reason - it's true.