For example, Quantcast. Konrad had done an applied stats company and I had a big data background. So we think about insurance fraud (sales cycle too long, concentrated customers), starting a quant fund (which is more fickle, the market or investors?), etc, or ad targeting.
Ad targeting. Big, fast growing market, and it's all script kiddies except for google (this was 2006). But where do you get the data? I knew that publishers hated comscore and Nielsen with a passion. So, free measurement service and provide targeting along with. Then, how to promote it? Using SEO. Create a web page for every site so that it shows up when a webmaster searches for his site name. Once you have have petabytes of data, hire PhDs and give them powerful tools. And voila, powerful as targeting with a unique data advantage and publisher relationships.
You want big market, fast sales cycles (aka easy customer decisions), fast growth, slow witted competitors, and most of all don't even start unless you know how you will promote and sell it. I'm partial to b2b because consumer is so random, it's a tipping point thing and there's almost never any technology involved.
Cool problems are cool problems. Find them, choose the one you can solve.