They really don't influence what I build.
Twenty years ago, they had a pretty big influence on what courses I tried to go see. However, the more I've seen of the rankings and the various results, the less stock I place in them. There are a few new courses in the GOLF DIGEST rankings, one or two of which I have absolutely NO interest in seeing, based on word of mouth reviews from others and on my own experience with other courses.
The existence of rankings MAY influence what sorts of projects I take on, although it's just one of many factors.
The only real influence rankings have on me is that they have too large a bearing on how much I earn. That's why they're so dangerous, and why most architects care at least a little bit about them, no matter what we say.