This is not particularly surprising. Computers have to work a bit harder to render Flash and similar content and the harder they work, they more energy they use. The same applies to other aspects of computing too - for example, your computer will use more energy when it's being used to perform resource-intensive video editing than when it's sitting idle of being used to write an email. That said, this is still something that will probably something which will come as a surprise to many people.
So, what's the best option? You could simply not install Flash, but then there would be content that you would be unable to see (you may not miss the banner ads, but there would probably be other forms of content that you would miss). A better option is to use an application that will selectively block these things. If you are using Internet Explorer, you can use TurnFlash to switch Flash on and off so that you see only the content that you want to see. Tools such as the MVPS HOSTS file will enable you to block other (non-Flash) unwanted ads. If you are using Firefox or SeaMonkey, check out NoScript and AdBlock Plus. Both will block unwanted content and help reduce your computer's energy consumption. All of these tools are completely free.
Using these tools will not only reduce your computer's energy consumption and make it more environmentally-friendly, it will also reduce the chance of it becoming infected with malware. These interactive elements are often used to spread malware, and so blocking them can will help keep you secure.
Don't expect to see a drastic reduction in your electricity bill. While Flash et al do cause your computer to use more electricity, they don't cause it to use all that much more (using power management settings will yield a much more substantial saving). But every little helps, right?