Does co-op, part-time, contract or agency work count toward the experience requirement?

It depends on the program. Part-time work can generally be counted on a pro-rated basis in many streams, as long as it was paid and matches your NOC duties. Contract and agency work usually counts too, if you can document paid hours and duties clearly. Co-op or work done while you were a full-time student is where most people get caught — several programs exclude it from the experience calculation. Read your specific stream's rules carefully and keep pay stubs, letters, and contracts to prove every hour.