I was having a bit of a Google (as one does) & I stumbled across this site:
Test cricket world champions since 1876
We're indebted to a gentleman called John Birch who, taking the first ever test as his start, has proposed a theoretical test world championship belt similar to the ones in boxing, whereby you become world champions simply by beating the existing champions. A lot less complex a method than the ICC test rankings, certainly.
Amazingly, Zimbabwe were once the linear world champs by virtue of their win over India (the Indians having claimed the title by beating Oz in their 97/98 home series), but NZ have never held the title & SA haven't for over 100 years.
The site was last updated in 2001, when India again became champions with a home win over Australia, so I've taken the liberty of updating the title holders:
2001: India: drew 1-1 with Zimbabwe in Zimbabwe (2 tests)
2001: Sri Lanka: beat India 2-1 in Sri Lanka (3 tests)
2001/02: Sri Lanka: beat Bangladesh 1-0 in Sri Lanka (1 test)
2001/02: Sri Lanka: beat West Indies 3-0 win in Sri Lanka (3 tests)
2001/02: Sri Lanka: beat Zimbabwe 3-0 in Sri Lanka (3 tests)
2001/02: Sri Lanka: beat Pakistan 1-0 in Pakistan (1 test)
2002: England: beat Sri Lanka 2-0 in England (3 tests)
2002: England: drew 1-1 with India in England (4 tests)
2002/03: Australia: beat England 4-1 in Australia (5 tests)
2002/03: Australia: beat West Indies 3-1 in West Indies (4 tests)
2003: Australia: beat Bangladesh 2-0 in Australia (2 tests)
2003/04: Australia: beat Zimbabwe 2-0 in Australia (2 tests)
2003/04: Australia: drew 1-1 with India in Australia (4 tests)
2003/04: Australia: beat Sri Lanka 3-0 in Sri Lanka (3 tests)
2004: Australia: beat Sri Lanka 1-0 in Australia (2 tests)
2004/05: Australia: beat India 2-1 in India (4 tests)
2004/05: Australia: beat New Zealand 2-0 in Australia (2 tests)
2004/05: Australia: beat Pakistan 3-0 in Australia (3 tests)
2004/05: Australia: beat New Zealand 2-0 in New Zealand (3 tests)
2005: England: beat Australia 2-1 in England (5 tests)
2005/06: Pakistan: beat England 2-0 in Pakistan (3 tests)
2005/06: Pakistan: beat India 1-0 in Pakistan (3 tests)
2005/06: Pakistan: beat Sri Lanka 1-0 in Sri Lanka (2 tests)
2006: England: beat Pakistan 3-0 in England (4 tests)
2006/07: Australia: beat England 5-0 in Australia (5 tests)
2007/08: Australia: beat Sri Lanka 2-0 in Australia (2 tests)
2007/08: Australia: beat India 2-1 in Australia (4 tests)
2008: Australia: beat West Indies 2-0 in West Indies (3 tests)