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!

Alternate ads - allows you to utilize your ad space in the event that Google is unable to serve targeted ads to your page.
Alternate Url - provides a 50/50 Revenue Share, full global coverage monthly payments automatic referral income, family safe ads, paypal supported and gives detailed stats.
AlterNut Ad - pays you a flat rate every month in return for you displaying thier ad rather than the PSA. Invite only.
Default Ads - load your affiliate or other ads into DefaultAds and generate a link to include in your Google Adsense alternate ad URL. They show their own ads 1 out of every 100 impressions for this service.
Adsense Chats and Forums


Inside AdSense blog - Official blog that posts new tips and information about new AdSense features.
Adsense Help - Google group for adsense support. Only posts from user ‘AdSensePro’ are approved by Google.
Digitalpoint Adsense Forum - discusses Adsense payments, guidelines, stats and reporting and much more.
Webmaster World Adsense Forum - Discussions around Googles Text Ad service AdSense.

AdRotator Wordpress Plugin - rotate your adsense ads with other affiliate programs like Chitika Eminimalls
Adsense Deluxe - offering advanced options for managing the automatic insertion of Google AdSense or Yahoo Publisher Network (YPN) ads to your WordPress posts.
Adsense Injection - inserts Adsense code randomly into a pre-existing blog.
Adsense Inline - insert adsense in blog posts
AdSense Widget for WordPress Sidebar - Google AdSense widget I designed for the new WordPress Sidebar Widgets plug-in.
Google Adsense Optimization Tips


Adsense Success Case Studies - detailing success stories from top adsense publishers.
AdSense Optimization for Forums - get higher CTR by a unique adsense placement strategy.
Blogtimize! - ad placement for blogs for higher CTR
Adsense Optimization Tips - General tips for better ads postitioning and earn higher revenue.
Adsense Webinars - online seminars that help publishers obtain the highest results from their implementations of AdSense.
How to increase Google Adsense CTR - simple tips on colors and ad placement can increase CTR.
The Best of Eyetrack III - What We Saw When We Looked Through Their Eyes. How readers scan a webpage.
How to Remove Public Service Ads - simple tips to help you remove non paying PSA ads.
AdsBlackList - will teach you how to seek, recognize and filter low paying google ads.
Yahoo Ads placement tips - suggestions to place Yahoo publisher network ads. Apply the same idea to adsense ads.
Rotate Google Adsense Ads Colors - helps to reduce Ad Blindness
High Paying Adsense Keywords - updated list of current highest paying keywords for Google Adsense.

Program policies, Terms and conditions - follow these rules.
Adsense FAQ - The Adsense support centre for official guidelines.
Adsense Tax information - how google collects and uses your tax information
Adsense Taxes - a free resource about paying income tax on Google Adsense Revenue.
15 Common Adsense Mistakes - Avoid these errors that could get your adsense account banned.
Ad formats - Official list of different types of ad formats you can use.
Webmaster Guidelines - will help Google find, index, and rank your site.
Report a policy violation - If you notice a site displaying Google ads that you believe is violating program policies, let them know.

Google Adsense Guidelines

Program policies, Terms and conditions - follow these rules.
Adsense FAQ - The Adsense support centre for official guidelines.
Adsense Tax information - how google collects and uses your tax information
Adsense Taxes - a free resource about paying income tax on Google Adsense Revenue.
15 Common Adsense Mistakes - Avoid these errors that could get your adsense account banned.
Ad formats - Official list of different types of ad formats you can use.
Webmaster Guidelines - will help Google find, index, and rank your site.
Report a policy violation - If you notice a site displaying Google ads that you believe is violating program policies, let them know.

This one is a bug, to be honest. My surname is French, and I prefer to write it out correctly with the accent grave on the first "e". Every page on my site would then include at least two accented letters, because my name shows up twice in the footer. On some pages my name shows up two or three more times.
Normally, this wouldn't be an issue. But on some pages the presence of the accented characters is enough to cause AdSense to display non-relevant ads in French. This happens whether the browser indicates a preference for French or not. When I reported this to Google, this is the answer they gave me:
Hello Eric,
Thank you for bringing this issue to our attention.
We are currently working as quickly as we can to address this problem. As soon as we have more information for you, we will email you again.
We appreciate your patience.
Sincerely,
The Google Team
Until this is resolved, I've decided to strip out all accents except on the pages that are actually in French.
Tip #4: Check your keyword density
Although Google doesn't release exact details as to how they determine the ads to serve on a given page, they do tell us that it's the text content of the page that matters, not the meta tags. Before serving ads on a page, then, you might want to check its keyword density. A good, free tool for doing this is found here: http://www.ranks.nl/tools/spider.html
This lets you fine-tune the page before exposing it to the AdSense crawler.

As explained in Why are ads displayed on this site?, most of the pages on this site display text ads from Google's AdWords program. To display these ads, a site must join Google's AdSense program. Joining is free, but not all sites are eligible to join. Once you're accepted, however, it's very simple to place the ads on your pages and to start generating revenue for your site. AdSense will serve ads that are generally very relevant to the content of a particular page. Here are some tips based on my experiences so far with the AdSense program.



Tip #1: Don't put ads on empty pages.



When I reworked my site, I built a skeleton set of pages that had no content, just titles and some meta tags. I displayed ads on those pages, however. Although all you see are public service ads at first, the very act of displaying ads on a page causes the AdSense web crawler to quickly fetch that page for analysis. A page with good content will thus begin showing relevant paying ads fairly quickly.
If you don't have any content, then, Google will have to guess as what your page is about. It may guess wrong, and so the ads that it displays may not be relevant. You'll have to wait until Google re-crawls the site for the ads to correct themselves. Here is what Google had to say when I asked them about how often the AdSense crawler updates a site:
Thank you for taking the time to update your site. New ads will start appearing on your site the next time our crawler re-indexes your site. Unfortunately at this time, we are unable to control how often our crawlers index the content on your site.
Crawling is done automatically by our bots. When new pages are added to your website or introduced to the AdSense program, our crawlers will usually get to them within 30 minutes. If you make changes to a page, however, it may take up to 2 or 3 weeks before the changes are reflected in our index. Until we are able to crawl your web pages, you may notice public service ads, for which you will not receive any earnings.
It's better to flesh out the page before you start displaying ads on it.

As explained in Why are ads displayed on this site?, most of the pages on this site display text ads from Google's AdWords program. To display these ads, a site must join Google's AdSense program. Joining is free, but not all sites are eligible to join. Once you're accepted, however, it's very simple to place the ads on your pages and to start generating revenue for your site. AdSense will serve ads that are generally very relevant to the content of a particular page. Here are some tips based on my experiences so far with the AdSense program.

Tip #1: Don't put ads on empty pages.

When I reworked my site, I built a skeleton set of pages that had no content, just titles and some meta tags. I displayed ads on those pages, however. Although all you see are public service ads at first, the very act of displaying ads on a page causes the AdSense web crawler to quickly fetch that page for analysis. A page with good content will thus begin showing relevant paying ads fairly quickly.
If you don't have any content, then, Google will have to guess as what your page is about. It may guess wrong, and so the ads that it displays may not be relevant. You'll have to wait until Google re-crawls the site for the ads to correct themselves. Here is what Google had to say when I asked them about how often the AdSense crawler updates a site:
Thank you for taking the time to update your site. New ads will start appearing on your site the next time our crawler re-indexes your site. Unfortunately at this time, we are unable to control how often our crawlers index the content on your site.
Crawling is done automatically by our bots. When new pages are added to your website or introduced to the AdSense program, our crawlers will usually get to them within 30 minutes. If you make changes to a page, however, it may take up to 2 or 3 weeks before the changes are reflected in our index. Until we are able to crawl your web pages, you may notice public service ads, for which you will not receive any earnings.
It's better to flesh out the page before you start displaying ads on it.