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It's almost an issue of free will.

Computers do the things they do because they literally have no choice. They can't choose what to do or what not to do anymore than the sun could choose whether or not to quit shining or the snow could choose whether or not to be cold.

Human beings, however, have the ability to do this, which is almost paradoxical; the ability to choose anything you want suggests that true randomness exists and the universe is non-deterministic, or at least that the universe allows non-determinism.
If the universe, however, is deterministic and not non-deterministic, then human beings really don't have free will and any thought that you did is simply a lie, or rather you had that thought because you were programmed to and had no choice in the matter.

As for me, I don't believe that. I think we do have free will, a precious gift granted to mankind by no less than God Himself.
Anyway, that's my personal opinion. Your mileage will probably vary.

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Aren't you ignoring the fact that all animals have free will, even though many are not self aware?

The ability to determine its next action [free will] may not necessarily indicate the level of an entities intelligence.

Most animals don't make/use tools, in the main, save useful adaptations and behaviours they have been endowed with. It is possible, however, someday we'll see an ape fashion a ladder and escape from a zoo.

It's been definitely demonstrated that humans can make human and inhuman tools. The ultimate inhuman tool could be SI/nanotech (would the acronym SIN be appropo?). Food for thought.

Aren't you ignoring the fact that all animals have free will, even though many are not self aware?

It may be that true intelligence would require both self-awareness and free will. And the free will question still puts us back into the old deterministic v non-deterministic question. Even so, I'm not entirely convinced most animals do have free will. They may, but I don't know how you'd prove that one way or another.

The ability to determine its next action [free will] may not necessarily indicate the level of an entities intelligence.

No system has the ability to know with certainty its next action. This is an elementary theorem used in many areas of mathematics and used so pervasively most people do not even recognize that they are using it. It is the reason, for example, that one can never guarantee with perfect certainty that something is in a particular state (the basic interest of transaction theory), though we treat very high probabilities of a particular state as "perfect certainty" as a practical matter.

I think we do have free will, a precious gift granted to mankind by no less than God Himself.

On the other hand, free will could be a complete illusion - try not to think of elephant for the next minute.