Interesting question.
Case One — Goals not Goal
When systems are developed, they are based on requirements. The goals of the system is closely coupled to the goals of the development. This is the first example. Few systems and few development efforts to construct them are goal driven. They are rather systems and processes that tend toward a set of goals. Rarely is there a single loss function.
Consider an animal. It's metabolic stasis system may generate what seems like a goal, a set of signals to other systems to find and eat food. At another time its temperature stasis system may generate what seems like a goal, a set of signals to other systems to build a shelter to enter. The notion that there is some goal to survive is inconsistent with the way neurological and metabolic systems actually interact. Survival, some would say, was the goal of the animal's evolution, but that is not technically true. It survived, not because survival was a goal but because each of its ancestors survived as a result of transient and recurrent command signals for eating and sheltering. There is no aggregate loss function. There is no single neural pathway that all these signals are funneled through. The animal's behavioral subsystems may share some components, but the mechanisms of intent are largely independent. It only appears to a casual observer that the separate systems are collaborating toward survival.
This is true of some vehicle automation systems. Collision avoidance is a system with a set of goals and routing is a system with a separate set of goals. The goals are decoupled even though they may share a CPU, vision systems, and a large number of functional components and computing resources.
These systems are goals driven, using the plural, not goal driven.
Case Two — Process of Elimination
Another type of AI approach that is not technically goal driven are genetic algorithms. They replicate and some of the replicants are eliminated, but the entities themselves have no goal. The elimination criteria is not technically a goal. It is the opposite of one. The appearance of replicants that are not eliminated after many rounds of replication and concurrent narrowing of criteria may achieve some goal of the person running the algorithm, but the algorithm itself has no representation of a goal but rather its opposite, the final criteria of elimination in the last round.
Case Three — Experimental Apparatus
Many AI experiments to discover the nature of intelligence and ways to simulate aspects of intelligence have the external goal defined by the researcher, but the system used in the experiment, the AI apparatus, is not driven by a goal. It runs goal-less.
Case Four — Toys
Whether toys for adults or kids, toys may arise with some goal in mind, to amuse in some way, but the AI within them has no goal. There is no loss function to minimize or reinforcement or wellness signal to maximize. It's behavior may be less amusing if it were goal driven. What makes it amusing is its ability to produce patterns associated with intelligence, but to no particular purpose. In some ways, much human conversation and creative art is like this. Too much purpose, and the level of amusement decreases.
Case Five — Robots That Mimic Postmodern Humans
Humans in postmodern society, the ones that are truly relativists and have rejected modernism, are not particularly goal driven. They tend to wander around and do things that are intelligent, however they may act goal directed and then destroy the product of the transient goal. Building sand castles on the beach is an example. Although this may not be the focus of current AI research, since there is so much hope placed in AI to do things for us, such does not exclude the possibility of future robots that build something and then destroy it to build something else, without some practical objective.