I'd add overhead presses and weighted pullups and pushups to squats and deadlifts. Bench presses are for impressing other gym rats. Overhead presses are much more beneficial for your shoulders.
If you're seriously training the basic lifts, you also need to do lots of accessory lifts to balance things out, and ideally have a professional teach form. I would argue that both overhead presses, and bench presses are valuable, and complementary for generally becoming strong. The bench press is unique in that it engages more of the upper body muscle in a single, coordinated movement than almost any other lift... some refer to it as the upper body equivalent of a squat. Overhead pressing is also valuable, but isn't a replacement for it, it's just different.