I LOVE pileated woodpeckers. They're huge! We had lots of those on my friends' property on Vancouver Island. I've seen some in Mexico too, but just the smaller ones, who are awesome nonetheless.
I bet I've had finches around, just never paid any attention to them. Same with the thrushes. It always takes someone else to infect me with their enthusiasm.
Hummingbirds are a common sight even in such a poisonous environment as Mexico City. (Not in New Zealand though.) Behind our apartment there is an abandoned lot with some 10ft tall weeds, where they love to hang out and feed on the flowers. They always like to come and check out our place too, but when they come in through the window they may have a hard time finding their way out again.