In my house, I don't "hear" whines. It's a foreign language that I don't understand. When any of my boys tried to whine at me, I looked at them with puzzlement and say, "Sorry sweetie, I can't understand what you're saying. You need to use your big boy voice." If the whining continues, I just say, "Sorry, but Mama doesn't understand. Come tell me when you find your big boy voice, okay?" Then I walk away and get "busy" with something else.
(I think the harshest thing you can (reasonably) do to a toddler is ignore them. They love, love, love to be the center of attention and NO attention is worse than negative attention. If a behavior gets them ignored, they learn pretty darn quickly NOT to engage in that behavior!) A side benefit of not allowing whining is that encourages children to build their communication skills. Whiney children tend not to verbalize what they want/need, they point, fuss and cry.
My big reason for wanting to raise non-whiney children (other than the obvious reasons) is because when I worked in the childcare industry I noticed that whiney children are the most unpopular kids with the adults - and are often likely to be more unpopular with their peers. Most adults get irritated by whining, and when an adult is dealing with a number of children they don't have the time or inclination to try to interpret whines. I darn sure didn't want my children's future Kindergarten teacher to have any reason to dislike or be annoyed by them!