"Leading research firm Gartner recently predicted that the cell phones and smartphones would overtake PCs as the most common devices used for Web access in the next three years. But many phones' Web browsers aren't quite up to snuff yet. Fortunately, there's a thriving industry of alternative browsers challenging handsets' default applications."
Among the many (yes many) that I have personally tried out, I've always come to rely on Opera Mini as the best and the standout performer but it does not play video. Bolt is a new entrant that does play video but is not as smooth or easy to use as the Opera Mini. UCBWeb is very impressive but still has some way to go. Apart from that the playing field is not just level but rather bereft of good performers.
Here is a good article going through the various options that mobile phone users and smartphone users have in terms of mobile phone browsers and yes all are free.