Pretty much what Shawnee said, +1.
Great deer calibers are:
.243 Winchester
6mm Remington
.250-3000 Savage
.257 Roberts
30/30 Winchester
.32 Winchester Special
Some not-so-thunderous larger calibers that enjoy very good reputation on deer are:
.25/06
6.5x55 Swedish Mauser
.260 Remington [added]
.270 Winchester
7x57 Mauser
7mm/08 Remington
.35 Remington
I highlighted some of the "better" ones, in my opinion.
Also .44 magnum or .45 colt in a rifle,
.300 Savage, .303 Brit, .30-40 Krag, .45-70 with light "level I" loadings, and 7.62x39mm with proper ammo are also good non-overkill choices, though a bit more on the stouter side of recoil than the bolded "preferred" choices. IIRC, the 2nd largest typical whitetail ever shot with a gun and recovered, and for awhile the largest, was killed with a .25-20 (neck shot), albeit with some tracking.
But killing a deer is
95% shot placement (hunter skill in the stalk, the shot, and anatomy knowledge - oh, and your rifle's accuracy & precision),
4.9% bullet selection (bullet construction needs to match the game's body type, ambient conditions, and velocity when it reaches the game), and
0.1% cartridge choice, once you get to .357 mag and above. So just throw a dart and pick a caliber. If you enjoy recoil, then get a .270 win or .30-06 (or heck, get a .300 maggie if you like recoil). If, like most people, you don't particularly enjoy extra noise & recoil, then go with one of our "lighter" recommendations.