Tamed?
At the end of the play, Petruchio wins a bet by proving his wife the most obedient. He had earlier talked about how he trained her like a hawk, attempting to justify his treatment of her, and Katherine shows her obedience by coming to him at his command. Following this, Katherine gives a speech on the importance of wifely obedience.
The play is often performed in such a way that it is clear that Katherine is ironic in her speech, or has simply learned that the best way for her to get her own way is to fit in with the expectations of society. It is certainly true that Bianca and Katherine move in opposite directions* in the play, the one from shrewishness to seeming obedience, the other from seeming obedience to a refusal to obey.
It is certainly true that Katharines' status has improved by being married. And it is also clear that the society that Shakespeare portrays is one where most women feel they have the freedom to speak their minds: Petruchio is very much an exception to the rule, as the other men find out when they lose the final wager.