For analysis the standard recommendation is baby Rudin, which I find dry, but it has good exercises and it's a good filter: it'll be hard to do well in, say, math grad school if you can't get through Rudin.

I feel that it's only good as a test or for review, and otherwise a bad recommendation, made worse by its popularity (which makes its flaws harder to take seriously), and the widespread "I'm smart enough to understand it, so it works for me" satisficing attitude. Pugh's "Real Mathematical Analysis" is a better alternative for actually learning the material.