I have a few favs, and here are my (not so good) encounters with them:
California Condor; July 19 and (maybe) 20, 2005; North Rim, Grand Canyon, AZ-One bird flew over me, 20-30 feet up. However, I was rushing to reach my dad, because he said he saw a condor (the bird flying over me!), and I was in such a rush, that I glanced at it and ignored it, To my later dismay when my dad told me that was the bird! Not the best, but a sighting. We also think we saw two the next day in Zion, Utah, even though we didn't now condors lived there. We ignored tham (AGAIN) until we later read about condors in Zion. Several experts confirmed our sighting via e-mail.
Snowy Owl; January 22, 2006; Jones Beach State Park, NY- Long one of my favorite birds, I searched for them multiple times in multiple winters. Finally, one visit, rangers told us about a bird that was right outside. We saw him well through binocs, and got two cruddy pictures.
Peregrine Falcon; Fairly Often Seen, but still, what a bird! Gives me a real rush when I see one.
Red-tailed Hawk; Often Seen, but still a favorite. I've had a few close encounters with them, too.
All of these birds will always be important to me!