As soon as possible in my opinion. It's not only good for them (self esteem, independence, etc...), but it's one less thing you'll need to worry about once they get it down right. Plus, it's so cute to see them pick and choose what they will and then get dressed. Obviously the younger your kids are at the time that they show an interest in dressing themselves, the more 'supervision' they'll need, but that enables you to make sure they are dressed appropriately for weather and activity.
My oldest was ready to dress himself by the time he was 2. He liked picking out his own clothes, and while they still end up backwards at times (he's 8 now), he is happy to dress himself and have control over what he wears.
My youngest isn't quite 2 yet and he has more interest in taking his clothes off than in putting them on himself, though he does like to 'pick out' his own clothes. I let him wear what he picks on days we're staying inside, but there are some Definite changes when it comes to going outside to play.
Hope this helped =)