There could be a couple of things contributing to this. My guess;
- It looks better
- Easier to style
- It's clearer where and easier to click
Fact of the matter is, styling-wise, radio buttons don't look good. On top of that, on the web, they're not stylable in any reliable way.
Add to that the fact that not everyone always makes the text behind a radio button a label, and you've got an element that's small, hard to click, and can cause a fair bit of frustration. This would be one of those cases where the people that mess up (the label bit) make it worse for the people that do it properly, as users start compensating and will automatically mouse towards the circle as opposed to the label.
That latter reason isn't probably nearly as important as the former ones though. They're just tough to style.
.edit: plus, bootstrap is quite popular and perhaps people have copied that pattern a bit.
.edit2: As for dropdowns, it's probably because having choices out in the open makes it easier to see what's coming then when you have to click first.