One of our clients recently wrote to us, "Tell me about Apple's Webkit and your thoughts on avoiding Flash."
I anwsered: Apple's webkit is the software that is the heart of their browser, Safari. It's what's called the 'rendering engine' that lays the web page's elements out on the screen. The other major open-source rendering engine is the gecko engine that powers the Firefox browser. Both are perfectly serviceable pieces of software. Indeed, Steve Jobs is disparaging Adobe's Flash technology here of late, especially for the iPhone and iPad. He's pushing the next generation of web standard, HTML5, as an alternative.
Unfortunately, no browser is yet 100% ready for HTML5 yet. My current release of Firefox (3.6.3) only scores 139 out of 300 points at http://html5test.com/, whereas the latest Safari (5.0) scores a bit better: 208. Don't even ask about Internet Explorer. So I'd say we're probably a good year or so away from being able to use the parts of HTML5 that will replace flash. We've always said that Flash is good, in its place, but shouldn't be overused. After a year or so, when more browsers are truly HTML5 compliant, we'll take another look.