I'm smiling, because I can imagine the little face they make when they say that, maybe punctuating it with a foot stomp!

When my kids do that, I let them know what the consequences of their actions are, and then follow through.

"Ok, I can tie your shoes for you, but if I do then I get to choose which shoes you wear," sometimes works, as they then realize that they lose some control over their choices if they have you do the work. I also make it clear that time I spend with them doing things they don't like, means less time I have to spend with them doing things they like. "Ok, but that means we won't get to the park as fast, and you'll lose five minutes of play time." I do give them time limits, and let them know what the consequences are, and later on if they complain I'll remind them that they chose to have me tie their shoes, lost 5 minutes of playtime, and perhaps they'll tie their own shoes next time.

I don't want to teach them that they must always do certain things by themselves, though. Because I ask them to do things around the house to help me, I try to develop a relationship where if they ask me to do something, and I have time, then I will probably do it. So far they seem to reciprocate.

I've also found sometimes it isn't stubbornness, but a request for special attention or contact. We have 5 boys, and I know that in the rush to get out the door sometimes one or more of them might feel alone in the bustle, so we do have to pay attention to their tone of voice, expression, and body language to see if there's some other reason than pure stubbornness.

I like Adam Davis's answer, but just thought I'd add another technique that has sometimes worked for me: Humour - for example, s/he asks you to put hir socks on for hir, you seem unsure about where they are supposed to go - do they go on hir ears, or perhaps hir hands? When I have done this it often ends with the child saying something like "No, don't be silly, they go like this" and putting them on hirself (trying to be gender-neutral here).