Lecture notes by George Cain: Basically introductory, going through residues and winding numbers.
Notes by Christian Berg, going through the residue theorem and then maximum modulus and Moebius transformations.
Notes by Curt McMullen, covering the first semester of a graduate-level complex analysis course, including the Riemann mapping theorem and elliptic funntions.
"Excerpts" from an Introduction to Complex Analysis, by B. V. Shabat that finishes with a proof of the Riemann Mapping Theorem.
A very basic book that just goes through contour integrals and power series
Notes by Christer Bennewitz that go into entire functions, and briefly treat the Riemann mapping theorem and the Gamma function.
Some brief notes by Dan Romik that include a lot of cool stuff like the gamma and zeta functions, and the prime number theorem.
Past Qualifying Exams from the University of New Mexico on Complex Analysis.
A resource page for Complex Analysis by James Cook taken from his course page.