There are two common sense ways that anyone can earn more per click with Adsense, so I'll list those first:
1) Relevancy
How relevant your ads are to your content plays a part in what you earn per click. Ads that are *very* specific to your content have a higher payout than general ads on specific pages - or general ads on general pages. How do you get the most relevant ads to show on your page? Make sure your page is specific, and well optimized for the specific topic or subject.
"On the Page Optimization" is what you want to focus on here. If you need some pointers on how to optimize a page,

2) Keywords
Adsense and Adwords go hand in hand. If the keywords you optimize your web page for are very competitive on Adwords... you will earn more per click. If your topic or keywords are NOT very competitive on Adwords, then you will earn a lower amount.
While it is not disclosed what the exact percentage is, your Adsense earnings are directly related to what the Advertiser is paying at Adwords for every click through. You are paid a certain percentage of that click fee when you generate clicks to the Advertisers site.
TIP: Use your Adwords account (or open one) to find out how much Advertisers are paying per click for any given keyword phrase.
That second method is a hot topic lately. In fact, people are building sites specifically for the purpose of earning Adsense revenue. I've even seen a few products on that topic, lately - one of them being SwapClix (mentioned in a recent blog post)
Here's the concept:
Find high paying keywords* and build a website around them, using Adsense as your source of revenue. Some people are even creating one-pagers (using reprinted material or free articles) that carry 3 Adsense modules on the one page... and then advertising these pages on Adwords (or other pay-per-click engines).
The goal is to bid on less competitive keywords in the same niche where you can get good placement for the minimum bid. You then advertise your optimized page, which will hopefully display the more competitive (expensive) ads. With this method, you stand to earn way more than you spend...
*High Paying Keywords - this is actually an inaccurate way to call it, though it's the popular phrase used in these discussions. What you are looking for is Competitive keywords. Meaning that the advertisers are paying higher bid prices for these words/phrases because it is a very competitive market. The more they are paying, the more you stand to earn ;)
Personally, I am not into building "junk pages"... but anyone with a brain can certainly figure out some very useful ways to put this theory into action - - while still providing a great resource to their target market!