That misses the point. Ask the original question again but replace the word "PIC" with "dog" and replace the word "IC" with "mammal". Remember that op-amps, regulators, and any number of other devices are also ICs.
That said: for complex tasks, logic ICs are more or less obsoleted by microcontrollers. There are simple tasks which might not warrant them, though. A while ago I built a foosball scoreboard which used logic ICs and some discrete transistor logic, just for the experience. It was my first digital circuit. If I had to make another one, I'd use a microcontroller. My board space would be halved, my part count would be maybe 1/3 of the original, it would be much easier to make configurable on the fly, and it would use less power. But I would still use hex buffer ICs on the longer control lines.
Torben