In most circumstances a .30-06 shooting 180 grain bullets should suffice. If you have reason to expect (75% or more probability would be grounds to 'expect') your shots will be over 300 yards, you might want to rely instead upon a Winchester .338 Magnum.
I would guess you are going to -- or already have -- receive a lot of different opinion on this question. I guess that means a variety of cartridges can and have killed elk before. Notwithstanding, an awful lot of elk have been successfully killed with the .30-06. If you've already got a .30-06, you are well equiped with a rifle suitable for hunting elk. If you want an excuse to add a new rifle to the battery, by all means, buy yourself a new rifle chambered for a cartridge burning more powder, pummelling your shoulder more, and shaking your retina more powerfully and/or a cartridge of larger caliber firing a bullet of greater mass. Buying a new rifle may contribute to the needed economic recovery. Buying a new rifle may cure your cabin fever or winter blues. Buying a new rifle, after you already own a .30-06, probably isn't going to substantially increase your prospects for killing an elk. At least that is my opinion.