While the 06 has killed every animal on the earth over it's 100+ year history you would be hard pressed to find a country that would allow it to hunt dangerous game such as a lion or cape buffalo.  I'm not sure on the jaguar but it should be OK with a zebra.  Most countries that allow you to hunt dangerous game have caliber restrictions in place and to hunt them it must be at least a 40 caliber and from a personal standpoint if I were to ever hunt them I would want some more power hunting something that is likely and wants to either stomp you into the ground or tear you to shreds before they are finished with you. 

This question came up on another Forum (Accurate Reloading)and the answer is summarized as follows, by African country:

Benin: no minimum rifle caliber Botswana: .375 caliber minimum for Dangerous Game

Burkina Faso: no minimum rifle caliber

Cameroon: .354 caliber minimum for Group 3 Big Game

Central African Republic: minimum rifle caliber of .375 for dangerous game or big game hunting

Ethiopia: no minimum equipment requirement for rifle hunting

Mozambique: no minimum equipment requirement for rifle hunting

Namibia

• Smallest caliber allowed 7 mm (.284).

• Minimum energy

• Big Game 5400 Joule

(Elephant, Cape Buffalo, Rhino, Lion)

South Africa

• Most provinces do not have a minimum equipment requirement for rifle hunting and rely on common sense.

• Some provinces require a minimum of .375 caliber for dangerous or big game hunting.

Tanzania

• The minimum equipment requirement for rifle hunting in Tanzania is .375 caliber for dangerous game or big game hunting.

 Zambia

• The minimum equipment requirement for rifle hunting in Zambia is .300 caliber for dangerous game such as Leopard and Lion.

• The minimum equipment requirement for rifle hunting in Zambia is .375 caliber for dangerous game or big game hunting such as Elephant, Buffalo and Hippo.

Zimbabwe

• Class A Game 5300 Joule Minimum caliber 9.2mm in diameter (Elephant, Hippo, Buffalo)

• Class B Game 4300 Joule Minimum caliber 7.0mm in diameter (Lion, Giraffe, Eland)

Your .30-06 would be legal for Zebra.

I don't know of any country that allows the hunting of Jaguars, and if they did, the US Fish & Wildlife Service would not allow the trophy to be imported into the United States.