I was checking out Wikipedia and I could see a British passport entitles to visa-free or visa-on-arrival for 173 countries despite colonization by the British. While USA ranks 2nd with 172 countries. Why?
I am not too sure about the “despite colonization” bit. I can't really see a pattern, one way or the other. Some ex-British colonies offer visas on arrival for British citizens (e.g. Kenya), some don't (e.g. India) and most treat German or French citizens in exactly the same way. And then for some reason, Luxembourgish and Finnish citizenships – but not British citizenship – are the only ones in Europe to enable a visa on arrival in India.
At the end of the day, the source used by Wikipedia (full table) has British citizens tied with Swedes and Finns and not far above citizens from a host of other European nations, Australia, the US and Canada. So the small differences that do exist might simply be accidents and the main fact in all this is that citizens from rich nations generally have easier access to other countries, whatever their colonial history.
Explanations for that might include the fact that it's good for business and tourism or that these countries have more means to secure agreements through diplomacy, foreign aid, etc.
One glaring difference between UK and US citizens (lack of visa-free visit or at least visa-on-arrival for Brazil) might however be explained. I can't find an official source for that right now but I think Brazil has a strict reciprocity policy and only grants visa-free access to citizens of countries that do the same for Brazilian citizens. Brazilian citizens can visit the UK without visa but not the US.