What's the range of latencies here? What types of projects really need the lowest latencies?

Financial trading algos where low latency is important were the initial big market for stream processing/cep. As another example, imagine you're trying to do real-time fraud detection based on click stream analysis. If your latency is low enough you can potentially prevent suspicious transactions ever happening instead of having to allow them and then recover them somehow later.

Storm is actually few years earlier. Its the first real-time processing framework before other projects showed up.

True, it showed up first. And then it stagnated for several years. Now it is behind the other alternatives.