Scavengers are probably the second most likely to develop intelligence, and I was definitely thinking in terms of carnivore vs. herbivore. Intelligent scavengers such as corvids and raccoons come to mind. That said, it's quite possible to scavenge with limited intellect. Vultures, for example, are somewhat intelligent, but not the extent of a dolphin, wolf, or primate. Additionally, a sufficiently intelligent scavenger will probably eventually turn to hunting. If you've got tool use, and are hungry for something dead, it's not a terrible leap to kill the thing yourself.

On the whole, intelligence in nature is largely focused on predicting another animal's actions, and planning to take advantage of that foresight. The benefit of being better at that than your peers is immediately obvious in a hunter: predict, hunt, kill, eat. For things that aren't doing the hunting, more passive solutions can be optimal: evolving faster escapes, or natural defenses such as being very large take less energy, and can be developed much faster, when compared to the rather energy intensive process of maintaining a large brain and raising intelligent young.