When faced with a tricky question, one think you have to ask yourself is 'Does this question actually make any sense?' For example you could ask "Can anything get colder than absolute zero?" and the simplistic answer is "no"; but it might be better to say the question itself makes no sense, like asking "What is north of the North Pole"?
I think when we're talking about "superintelligence" it's a linguistic construct that sounds to us like it makes sense, but I don't think we have any precise idea of what we're talking about. What *exactly* do we mean when we say "superintelligent computer" -- if computers today are not already there? After all, they already work on bigger problems than we can. But as Geist notes there are diminishing returns on many problems which are inherently intractable; so there is no physical possibility of "God-like intelligence" as a result of simply making computers merely bigger and faster. In any case it's hard to conjure an existential threat out of computers that can, say, determine that two very large regular expressions match exactly the same input.
Someone who has an IQ of 150 is not 1.5x times as smart as an average person with an IQ of 100. General intelligence doesn't work that way. In fact I think IQ is a pretty unreliable way to rank people by "smartness" when you're well away from the mean -- say over 160 (i.e. four standard deviations) or so. Yes you can rank people in that range by *score*, but that ranking is meaningless. And without a meaningful way to rank two set members by some property, it makes no sense to talk about "increasing" that property.
We can imagine building an AI which is intelligent in the same way people are. Let's say it has an IQ of 100. We fiddle with it and the IQ goes up to 160. That's a clear success, so we fiddle with it some more and the IQ score goes up to 200. That's a more dubious result. Beyond that we make changes, but since we're talking about a machine built to handle questions that are beyond our grasp, we don't know whether we're making actually the machine smarter or just messing it up. This is still true if we leave the changes up to the computer itself.
So the whole issue is just "begging the question"; it's badly framed because we don't know what "God-like" or "super-" intelligence *is*. Here's I think a better framing: will we become dependent upon systems whose complexity has grown to the point where we can neither understand nor control them in any meaningful way? I think this describes the concerns about "superintelligent" computers without recourse to words we don't know the meaning of. And I think it's a real concern. In a sense we've been here before as a species. Empires need information processing to function, so before computers humanity developed bureaucracies, which are a kind of human operated information processing machine. And eventually the administration of a large empire have always lost coherence, leading to the empire falling apart. The only difference is that a complex AI system could continue to run well after human society collapsed.