In Aurora, Colorado, the HOAs wield a lot of power. Elected officials in the city generally come from leadership positions in the larger HOAs, and not the business community.
For projects that require Planning and Zoning Commission approval, all HOAs are notified within a mile of the site. Referral cards are sent back to the planning case manager, with all comments included in the planner's staff report. The HOA can choose to receive copies of resubmittals. For potentially controversial projects, the planner has the option of making neighborhood meetings with the HOA part of the review process.
The HOA doesn't approve development cases, but since they have a lot of power, their comments (and opposition) carry plenty of weight in the review process. Several times, when I was a planner in Aurora, I'd recommend approval for a project, while adjacent HOAs would be opposed. HOA reps and lawyers showing up in force to P&Z meetings were common occurences. The P&Z Commission would more often than not side with the HOA, and vote for a denial recommendation.