My current background in analysis is approximately the material in Folland's Real Analysis. I've also read the Analysis text by Lieb and Loss and I also took a graduate level class on complex analysis, which went up to Big Picard and some Nevanlinna theory. For my own amusement I've thought about furthering my knowledge of general analysis.
I've heard wonderful things about Stein's book on Singular integrals and his Fourier analysis on Euclidean spaces. Would these be an interesting next step? I'm especially interested in learning more about harmonic analysis and especially learning enough to understand the modern language of these fields.
EDIT: Here's maybe a more concise way of phrasing this questions: What's the core knowledge that every graduate student in analysis, regardless of specialization, at a top school is expected to know? What would be a reading list?