Tire wear only shows up in endurance races as the others have said. I'll add this as well: There is no actual difference from hard to super-soft tires when it comes to the way they wear out. There is only a difference in grip and friction.
In other words, hard slick tires don't offer as much grip as super-softs, but if you enter an endurance race on super-soft tires, they'll last just as long as hard slick tires. Why? Because someone apparently screwed up with the game programming.
GT1 & GT2: tire wear in endurance races only. In GT2, the programming is screwy--soft tires last about as long as hard ones in simulation mode.
GT3: Any event with more than 3 laps has tire wear if I remember correctly. Off-road races do not have tire wear at all.
GT4: All races (2-lap sprints to endurances) include tire wear. Some of the "Special Condition" events do not, though. I personally like this. Even a 2-lap race, you have to adjust your driving style because in the first lap your tires will be cold but in the 2nd you'll typically have more of a safety zone when cornering. The Ai knows this too, and you'll see them drive harder as races progress. 👍
*stammers incessantly* Perhaps all the cars in the race are established for being incapable to waste their tires in such races, therefore the feature was deleted for that event.
Oh I forgot about arcade tire wear..it's different from sim mode. I think you can make tire wear in Arcade mode stronger or weaker, right? Man it's been so long since I fired up GT2 arcade...