In a perfect world where money was no object, I'd have something like this:
1. 22LR Pump or Lever action, iron sighted. For close squirrels/rabbits/misc. varmints (Marlin's excellent 39A would be appropriate here, or a Remington Fieldmaster in a pinch)
2. 22LR Bolt action, scoped. For further squirrels/rabbits/misc. varmints. (A Browning T-bolt would be my dream, but an older Marlin tube fed would do)
3. 220 Swift/ .222 Rem/ .243 Win (pick one) single shot scoped, or bolt action, scoped. For medium to large varmints (Ruger's No. 1 in 220 Swift is my pick here)
4. 7x57 Mauser/.270 Win/ 30-06 Springfield Bolt action, scoped. For deer/larger game (Ruger M77 or Remington 700, in '06 for me, please)
5. 1894 Winchester in 30WCF; for any situation that might require fast follow-up shots on offensive critters. Others would prefer an AR-15 for this use, myself not so much.
Realistically, a person could get by with three rifles:
1. Rimfire rifle of some description, scoped or iron sights. Probably needs to be capable of using shorts, longs, and long rifles, and decently accurate.
2. Lightweight, light caliber repeating rifle, scoped. Bolt action will be most common, but most will choose an automatic here.
3. Midweight, medium caliber repeating rifle, scoped. Again, a bolt will be the common choice. Some folks might like a pump here, and others an automatic. It depends on the area.
In theory, a battery of three rifles in appropriate calibers will take everything from squirrel to moose in N. America; I prefer the first five I listed because, as we all know, "variety is the spice of life".
Mac