I remember reading an article years ago about .30-06 being able to take everything from rabbit to elk with the right loads. While I wouldn't go that far, I still think .30-06 is tough to beat.

My 5 favorites are:
12 Gauge shotgun in a 3" chamber
.22LR
.223 Remington
.30-06 Springfield
.375 H&H (not really common in the lower US states, but very common for big game)

However, I also like .17HMR, .22-250, .243, .270, .30-30, .308, .300 Win mag, .338 Win Mag, .45-70, and a bunch of others.

With those first five you can take on game anywhere and they're all relatively common. However, they're also not perfect. For example, .223 isn't quite as flat shooting as .22-250. .30-06 is the same way when compared to .300 Win mag, however it's slightly better than .308 (but, .308 is slightly smaller, making it easier to carry more, and can often be slightly cheaper).

I try to stick with calibers that are common and multi-purpose. There are a lot of wildcat rounds that are awesome for their specialized purpose, but difficult to find and expensive.

There is always a compromise, and therefore one has to decide what their requirements are and what best fills them. There is no magic bullet that can do everything perfectly.