UPDATE NOV. 2011 - Adobe has officially ceased development of Flash for all mobile devices. As a result, you can feel as close to 100% certain as possible now that Flash will never come to the iOS.
That doesn't quite mean that you can't use Flash in some ways. Check out these Flash-enabled web browser apps for some options.
As of March 2010, there is no Flash player for iPhone. Not because it doesn't exist or isn't technically possible (Adobe has created the software), but because Apple refuses to allow Flash onto the iPhone OS (and, since Apple controls what can and can’t be installed on the iPhone via the App Store, it can prevent this).
Apple charges that Flash uses up computing and battery resources too quickly and that it’s unstable, which leads it to cause computer crashes which Apple doesn’t want as a part of the iPhone experience.
Apple's blocking of the Flash player for iPhone is a problem for any web-based games that use Flash or service like Hulu, which stream video online using a Flash player. Without Flash for the iPhone, those sites don't work.
So far, Apple hasn't budged from its position (and seems to be waiting on the Flash-free standards in HTML5 to replace some of the features Flash offers to websites). Whether Apple or Adobe wins this high-tech tug of war remains to be seen.