The first answer is Google's Android, if we're looking at smartphone OS market share. The second is Apple's iPhone tied with Research in Motion's BlackBerry, if we're looking at smartphone manufacturer market share.
Let's look more closely at the numbers. Android has 29 percent share (broken down into 12 percent for HTC, 10 percent for Motorola, 5 percent for Samsung, and 2 percent for Other). Both iPhone and Blackberry have 27 percent. Microsoft, HP, and Symbian are not a threat, yet.