America, Canada, Argentina, and Brazil are almost completely dominated by the colonizing populations. (Here I'm counting slaves as one of the 'colonizers' since they are not native) However we do not see permanent British, to just take one, populations stay around to modern times in India, Malaysia, Hong Kong, etc.
Why wasn't this the case? Am I wrong in grouping Australia and N.Z. in with western hemisphere colonization? Were countries like South Africa the rule instead of the exception? Did the goals of colonization change? If so how?
This is not my field, so I'm sure somebody else could give you a much more in depth answer. But the simple explanation for the Americas is basically disease coupled with proximity. There's a lot of argument about exact percentages, because it's hard to establish the exact pre-Columbian population of the America's. But nevertheless huge percentages of that population certainly died out due to the introduction of new, virulent microbes that they hadn't encountered before. This left large areas of land far less populated than they had been, and the populations far less able to defend those areas. Compare this to someplace like India, where there are tons of people. If the English had wanted to colonize in the same way that they colonized Massachusetts and Virginia, they would have had to actively displace millions of people.
The colonies in "The New World" were also a lot closer to Europe than, say, Hong Kong. Add those two things together, and a lot of people who want to leave Europe for whatever reason are going to gravitate to the Americas and be able to establish a strong foothold.
1491 by Charles Mann has a pretty good overview of the effects of disease on the native population of the Americas.