Discuss the mystical art and science of product pricing.

My challenge with pricing is that it's hard to experiment with it. You can add new features, try different headings, and play with most things but you can't keep changing your pricing.

Depending on what you create and who you sell it to you may have tremendous flexibility in pricing.  The most common mistake that most make with pricing is starting with a price that is too low.  It's important to understand the impact (business value) that your product/service has on your customer.  Unfortunately though in some cases price is already determine by the market.

Flexibility in picking your price, or changing your price?

For web applications (my field) it's hard to adjust.
 

Agreed.  There are web apps that provide extraordinary value that are free or are sold at a ridiculously low price.  The bar has been set and we have to figure out other ways to monetize our products.  Facebooks apps might be an example of this.  Who cares if you have 2,000,000 users of your app if they're not spending a dime?  Might be good resume fodder but does it make any money?  It's kind of like rocking in a rocking chair.  There's a whole lot of movement but you're not getting anywhere.

Another point on pricing web apps.  Just because it's delivered over the Internet does not, by default, mean it should be free or Wal-Mart priced.