Push-ups are like the squats of the upper body -- they work practically everything. In fact, NASM-certified personal trainer Rachel McMichael says that pushups are hands down one of her favorite exercises because, “Not only do they work so many different muscles at the same time (shoulders, triceps, chest, core, and quads), they can be modified to any level. Modifications include wall push-ups, knee push-ups, triangle push-ups, incline push-ups, and so many more."
While push-ups work the front half of your upper body, pull-ups work the back half -- your shoulders, lats, rhomboids and biceps. Technically they’re not equipment-free, as you do need access to some sort of bar, but you don’t need to buy anything. I performed modified pull-ups today at a park today by using a swing as my "bar."