The AND OR NOT gate is used in the design of counters where you need to decode the present state to decide the function of an individual flip-flop on the next clock edge.
Ultimately, all logic circuits can be built using many of just one type of universal gate. Could be a NAND or a NOR gate. The inverting function in these gates is essential (can't be done with just AND or OR). From this one type of gate you can construct flip-flops, counters, micro-controllers, digital video decoders, or anything! Or you can use both types of gate. That's how all digital logic circuits are made!