How late in a human pregnancy can a zygote split?
Identical twins

Twinning occurring at the two cell stage or afterwards, up to and including the 16 cell stage, which translates to days 1 to 3 after fertilization, results in diamniotic, dichorionic twins. 

Twinning at the 32 cell stage (day 4), up to  and including day 6 results in diamniotic, monochorionic twins. The majority of identical twins split at this stage. 

Twinning from day 7 up to day 10 results in monoamniotic, monochorionic twins. This is rare and only accounts for about one percent of identical twins. 


diamniotic: twins have separate amniotic sacs 
monoamniotic : twins share one amniotic sac 
dichorionic: twins have separate placentas 
monochorionic: twins share the same placenta 


Conjoined twins

This is where things get a bit fuzzy. While some sources say that conjoined twins occur when the twinning event takes place after day 10, others say conjoined twins are created when 


  the twinning event occurs at about the primitive streak stage of development, at about 13–14 days after fertilisation in the human


It is very likely that because of the rarity of conjoined twins (one in 200,000 live births) there isn't enough data available on the very early embryogenesis. 

Sources and further reading:

The embryology of conjoined twins

Twinning

Conjoined twins