When I started hunting I lived in Northwestern Colorado and I asked the locals that I worked with this same question. At that time the only game that I knew that I would be hunting were Mule Deer and Elk. They advised me to get a .270 Win or .30-06. I chose the .30-06 and for about 10 years, I used it for everything from prairie dogs to elk.
For many years I wanted a 7 mm Rem mag, but I couldn't see that it was any better than the standard old .30-06.
Now, 50 years after I bought my first centerfire rifle (30-06), my favorite rifle is my .300 Weatherby that I wish I had bought 40 years ago. My safe now also holds rifles chambered in .223, .22-250, .257 Ackley, .270 Win, 7mm Rem mag, .30-30, .308 Win, .30 Gibbs, and .375 RUM. I shoot some of these more than others, and while most of them have big game notches in them (figuratively speaking), I usually only pick one of them for a specific animal.
Todays gun market is full of a huge variety of cartridges, but for the average North American hunter, I think its hard to beat the .30-06.