Never used a sippy cup in the first place.
When DD starting eating, she started using a real cup. She could drink from it on her own just fine at 6mo.
http://www.flickr.com/photos/lovecat...7600330803313/http://www.flickr.com/photos/lovecat...7600330803313/
Of course there were occasional spills, but that's part of the learning process. I firmly believe that if they're always given sippy cups, they learn that they don't HAVE to be careful with their drinks. So it's a harder transition when you do want to ditch them.
In contrast, if they use a regular cup from the beginning -- especially real glass cups -- they learn to be careful.
I think this is one of those things where something well-intentioned for convenience (I think sippies are great for in the car, for instance) ended up taking over as the DEFAULT situation for all circumstances. Babies never used to "need" sippies as their
primarydrinking utensil for the first 2-3 years of life. Perhaps eager to avoid a bit of mess, we started using them more and more. Until we forgot that there was ever any other way of doing things. (Same as the usual method of starting solids, with purees and spoonfeeding that they don't need, for instance)
This is also related to a general idea that babies and toddlers are capable of doing much less than they actually are, and that we have to 'help' them (either with parental assistance or with special products) far more than they really need. I wouldn't see pouring water as a remarkable ability for a toddler -- oh of course it's really cool

I grinned and cheered as my daughter did it as well. Just that it really is something "normal" that we've kind of forgotten, since we're always trying to protect them from having difficulties or making messes or whatever...
Anyway. If the question is "what age is best to stop using a sippy", I don't know if there is an answer, because there isn't really any age where they should
start using a sippy -- in the sense that there isn't a CORRECT age, I mean. There's no natural developmental timetable to using them. If we decide that we're going to use them because the convenience is worth any negatives for our particular family, we have to do it with that recognition.
If the question is, what age are they able to use a regular cup? I'd argue, any age.
For the original poster, perhaps a suitable transition would be to use a water bottle, like the stainless steel bottles with a basic sport top? Or with a narrow top opening, where they usually will put the whole top in their mouth? That might get her used to the different kind of flow. Or maybe just keep giving her a regular cup at every meal and let her figure it out by observing and imitating. I'm totally onside with those that think sippies should just be for travel, not for the table. I actually don't even think they should run around the house with a constant sippy... they can always return to the kitchen for a quick drink when they need one. But that can come down to family preference and choice. But if you're wanting to get rid of it, I can only suggest to keep trying. She does have the ability to figure it out, she just needs some practice.