I'm a firm believer that the single most useful caliber that exists is the .22lr. If I had to go down to just one gun to do everything with, it would have to be a .22. The only thing that the .22 is the best caliber for, is hunting small game like squirrels and rabbits. In a survival situation though it will kill anything with good shot placement. I'd rather try and kill a deer with a head shot from a .22, than trying to fill the pot with small game shot with a 30-06. If you factor in cost and availability, you can buy two bulk packs of 550 rounds for the same price as one box of most centerfire calibers. My favorite .22 that I own right now is a Ruger 10/22 and if I was forced to go down to just one gun, this would be it. The one problem that I do have with the 10/22 is how finicky it is to different brands of ammo. The gun will shoot Remington golden bullet ammo 100% of the time, but with Federal red box bulk pack it will jam once every 15 or 20 rounds. Someday I'd really like to get a Marlin 39A which should combine reliability with high capacity. With the jamming issues though, I don't think that the 10/22 fits the original question about most reliable.

Now that I've rambled on about the most reliable caliber when the original question was about the most reliable gun, I'll try and answer the question. It's hard to pick one overall since they all were bought with different intentions in mind, but I'll list my "go-to" guns for each purpose. Never once have any of these guns failed me.

Home defense - S&W model 19 .357 Magnum
Concealed Carry - Ruger LCP .380 acp
Deer Rifle - Marlin 336SS 30-30
Big Game Rifle - Remington 700BDL 30-06
Slug Gun - Marlin model 55 12 guage
Turkey Gun - Remington 870 12 guage
Bird Gun - Mossberg 500 20 gauge