I have a yellow-nape Amazon who loves walnuts but will eat most other things with relish as well (excitement, not pickle relish!). She used to be crazy about peanuts in the shell, until I learned that it's not wise to feed her those due to mold in the shell. Some of her other favorite foods include tofu, red pepper, veggies with a little tahini salad dressing (she'll eat them plain too, but throws them away in anger if she sees me eating a salad with dressing), apple, pasta, corn on the cob. She used to love broccoli and would say "broccoli!" when she wanted food, but then at some point decided that she didn't like broccoli anymore, and also stopped saying the word. Weirdly, I too went from loving broccoli to being wary of it, about a year later... but I'm digressing! I give her dates as treats, because she loves them but I'm concerned about the high sugar content.
Obviously she loves sweet foods like tapioca pudding, banana bread, apple crisp, etc. but those are a very rare treat. I am more or less on a macrobiotic diet and don't eat much added sugars, and when I do make desserts they tend not to be very sweet. This is good for my bird as well as for my health, because we have almost the same diet! She always has pellet food in her cage, but I also give her a little bit of every meal or snack I have. If I didn't she would have a fit. So with this arrangement, we keep each other healthy.
Another thing I've just remembered is that she loves garlic. Whenever she sees me peeling garlic in the kitchen she gets very excited and starts screaming for me to give her some. One time I was peeling it with her on my shoulder, and she jumped over and snatched the clove out of my hand and tore into it, devouring the whole thing and squealing with delight. She did, of course, reek of garlic for the next day. Now I make sure to hide around the corner when I peel garlic, so she doesn't know.