My DD has been able to drink (without help) from a normal cup since she was around 2 I think.. she could drink from it before that but not without me hovering around her and she would usually end up dumping half of it.
. But we didn't really give it to her on a regular basis until more recently (she's 3... and her manual dexterity still isn't amazing :P). I still give her a sippy cup in our playroom and out and about etc. I only give her a real cup to drink from at mealtimes when I can trust her to not be carrying it around with her!