I have long wanted to, but have never actually got to, teach a differential-equations course from Hubbard & West (http://www.amazon.com/Differential-Equations-Dynamical-Appro...). I thought that there was an article in Math. Mag. about their approach via "fences and funnels", but MathSciNet only knows about a 1995 CMS conference proceedings: http://www.ams.org/mathscinet-getitem?mr=1483923 . EDIT: The article I wanted (which has the same title as the proceedings article above) is actually in College Math. J.; it's http://www.jstor.org/stable/2687507 .

Another, I think, slightly gentler approach along similar lines is Blanchard, Devaney, & Hall (http://math.bu.edu/odes). The pedigree for this latter is very good; Devaney gave the (as far as I know) first rigorous mathematical definition of chaos. I have taught out of this one a number of times, and very much enjoy it.