There are still many websites that use flash to display content. Some of these use flash video. Others are flash games which are much richer than html games. Playing flash on an iPad is not possible normally, however there are a couple of ways to run flash on an iPad.
Method 1: Jailbreak your iPad
Not recommended. Jailbreaking your iPad will prevent you from downloading the latest OS. Jailbroken files also run the risk of hosting viruses or trojans. If you are still intent on jailbreaking your ipad, there are full instructions on how to jailbreak your iPad to play flash on Endgadget.com. Essentially, you run Spirit and then install the Frash plugin on your jailbroken browser. Frash is not perfect, it cannot run all flash content and videos sometimes don't work, but in general it seems to handle most flash games.
Method 2: Flash Supported Apps
There are a number of apps available which work by creating a remote desktop session to a browser hosted on a different platform. The major ones are:
Nominated for Best iPad Browser on About.com Readers' Choice Awards 2012, version 4.4 includes support for retina displays. Uses a firefox browser. Data is SSL encrypted to provide a secure browser sesson. The basic app purchase allows for 10 minutes of ad supported browsing. 30 days unlimited browsing will cost you an extra £2.99 or for a years unlimited browsing it's £34.99
Splashtop remote browser
Similar concept to cloudbrowse, except that it uses your own PC or mac browser to display in the ipad. It's very resource hungry on your PC, and supports Windows 7, Vista, and XP, Mac OSX 10.6+ (Snow Leopard or Lion is required for Mac users). The free version gives you 5 minutes of browsing time per day. Main advantage is that you can configure the browser for your requirements, including java support if you want to play games like Runescape. Disadvantage is that your computer has to be left on for it to work and will not work when connecting to a different network.
Not a flash browser per se, but can play flash videos by downloading and transcoding flash content to be stored on their servers. Makes claim to have over 200,000 websites converted already. Will not play flash games, or other flash content.
Photon Flash Player
Uses native browsing for non-flash content and remote browsing for flash content. You have to remember to click on the lightning bolt icon to enable the flash browsing in streaming mode and for viewing video, you need to crank the bandwith setting all the way up to 6. Not the most user-friendly flash viewer, but having mixed mode browsing is a nice touch.
Price: free / £2.99
This is by far the best flash browser that I've tried. Like cloudbrowse it uses a remote web browser session to a firefox brower. Unlike cloudbrowse, you don't have to pay a subscription. The basic app is free for 10 minutes per day for 7 days (which will be more than enough to allow you to evaluate the product) and if you want unlimited browsing it's only £2.99. Only downside is that it requires a wifi connection (although with streaming browser services, you would'nt want to use an expensive 3G tariff). iSwifter also has a nice opening screen with Google and Facebook games on there. Only downside is that there is currently no java plugin in the browser.
Whats the best way to play Flash on an iPad or iPhone?
Overall I would recommend iSwifter as the best method to run flash on an iPad. It's relatively cheap, handles flash well, and plays both flash games and flash videos. If you need to run java-based content and games, you are better off using a different app like cloudbrowse or Photon.