Just want to chime in with another book that hasn't been mentioned so-far: Philip Hartman's Ordinary Differential Equations. I am slightly ashamed to say that I still haven't read all of it, but it is the one that is on my shelf that I reach for if I need to look something up about ODEs.

From what I know it is somewhat similar in depth as Hale's book: i.e. covers some of the same topics Dan Blazevski listed below.