How you find an AdSense Niche?
 

Make a list of the topics that you can create competitive content for. (Example: if the topic is "chemistry" and you pronounce "cation" with a "sh" sound in the middle, then you can't really create competitive content for that topic. :-) If the list is empty, then you're done! (That means it's time to look into multi-level marketing schemes instead of AdSense.)

Pick a topic from the list.

Check the obvious keywords related to the topic in the Overture bid tool and see if more than a couple pay more than $1/click. If not true, go to Step 2.

Now search for those keywords in Google to see how competitive they are. If the page 1 SERPs for those keywords all have >10,000,000 hits and >PR6, and you're starting with a PR0 site, then it's probably going to take you years to rank for those keywords, so go back to Step 2.

Now you've found (probably after quite a long search) that rare thing: a non-competitive topic that pays well. At least, you think that's what you've found. Time to put it to the test and build a website.

Ooops, too bad, the sandbox effect (not saying there is a "sandbox", just saying that as a rule, new websites have trouble ranking well) means its likely you won't be able to rank for squat on this website for quite a while. Put 6 months into it developing content, then go back to Step 2 again and start trying to make your 2nd website while you let this one "age", with only minor ongoing development effort.

My niche(s) found me. I built a site with a wide variety of subjects and formats. I began in January 2002 and in August of 2004 I noticed certain pages drawing more traffic than the others. I built upon those pages and those subjects. I began with only subjects that I had at least a passing interest in, but I never would have guessed which niche(s) would have paid off for me had I not done it this way.
I did operate the site as a hobby for two years and it was an additional six months before AdSense began paying well for me, but that's how I did it and I'm very pleased with the site and its returns now.