The gun with the most kills in my house is my 20ga H&R UltraSlugger. The most kills for a weapon in my house goes to my 2009 Rytera AlienX (bow). Between the two almost a hundred kills on deer.
I have taken deer with my AR15 and LR-308. Even with the .223 and 20 rounds loaded guess how many shots each has taken per deer. One. Don't let either the caliber or the capacity worry you. Just put the shot where it needs to be and eat some venison.
Here you go. The deer are tiny, but I am not a picky guy with 16 tags to fill each year. This just a few of the kills as I don't take one of each and every kill, but I have more should more proof be needed.
150yds H&R Ultra.
185yds H&R again.
226yds H&R once more. Longest shot with it on the smallest deer (before I put my scope on it, I thought it was a yote needing salvation)
25yds Alpine Micro. Even my daughter agrees only one shot is needed.
My other daughter got one with a single shot shotgun and muzzleloader so I think we can verify no need for second shots. 8 deer this year alone, and only one was with a repeating firearm.
Side note: I never realized how popular the H&R's were until this thread! Mine is a match for about any muzzleloader, and pretty much negates my need for a rifle in most situations. Just costs a bunch to shoot so it gets sighted, range checked (for each range out to 250), and put away after the season. My true "hunt only" gun where as my others get range time year round.