We started giving my daughter a sippy cup at 6 months. BUT it was ONLY for juice and water...and the bottle was ONLY for formula. We were told only 4 oz of juice a day so we would mix 2 oz juice with 2 oz water and that way she could have it twice. She didn't mind it at all because nothing was "changed" it was only added..
Around 9 months we started moving to only using the bottle before bedtime and when she woke up. The rest of the day she was given all drinks in a sippy cup. We had no problems here again I think it was because she still had the familiar comfort during low times of the day.
At 12 months we threw all bottles away. She again gave us no problems. At a year and a half we started playing with big girl cups to give her practice. By 2 she used straw and lid cups on outings and she used big girl cups at restaurants and home. She is 3 now and only uses big girl cups...and we spill more than she does!!! ha ha
I think all children are different and will accept the sippy cup differently as well as different ages. But the important thing is be when you start it, be consistent! Otherwise your child will learn that if they fuss you will give in. It seems that when you are consistent with children, they are more secure, and in turn are more accepting to changes.
Another good idea is to make it fun, when your child is old enough to point and choose, pick up two fun cups and ask them which one they like. (Only give them as many choices as their age, 2yrs-2 choices, etc) otherwise they become overwhelmed and reject all of them)