Internet Explorer requires a Windows liscense, so it’s not exactly free. Also, Opera isn’t free to an OEM integrating it, it actually costs money, such as mobile phone operators. In fact, there are very few free mobile web browsers.
I personally have several web applications and also specific issues with FireFox that prevent me from using it full time. I use a combination of IE7, Opera and Safari, depending on platform and application. If I had to pick one, I’d be using IE because of the ActiveX functionality that’s lacking on any alternatives.