Its very typical for a three-year-old (and even older) but that doesn't mean you have to just tolerate it. Constant whining and complaining are socially unacceptable behaviors that you have to teach your children to stop doing. My oldest son (almost seven years old) is a TERRIBLE whiner and we've been battling it since his toddler years.
As soon as whining comes out of his mouth, we simply say, "I'm sorry, but I cannot understand you when you talk like that" or, "I'm sorry, but I can't hear whiny tones so you'll have to talk like a big kid". That usually stops him. Half the time, he doesn't even realize he's talking in a whiny voice.
As for the obnoxious whining where they simply want to annoy/punish/aggrivate you until you give in, we do either a time-out or even the occasional spanking when they continue to disobey when we say "stop whining".
Its an uphill battle, and its sooooooo frustrating. But it does get better with age.