Like most of the other posts, around 18mos or so we only used "open cups" during meals. Essentially we said 'sippies' were only for first am or at bedtime. When I refer to sippies here, I'm saying true sippy cups, not sport bottles or straw cups. We used this as a "table" rule. We bought some different plates and made a big deal out of the "new" tableware for big kids.
We used plastic dixie cups at first, or small plastic cups (like the "kids" cups from Fridays, Go Roma, etc). What I didn't like about Dixies is that the kids can squash them or crack them.
We continue to use sippies or straw cups, just for the spillproofness of them - and my kids are 4 and 6. I do not let them walk around with the cups. It's just while they wake up in the am and at nighttime for a cup of water bedside. We do not use "the piece" inside that prevents a spill when knocked over. I just don't allow "open cups" in our family room or in bedrooms for the kids - way too much trouble. This way if a cup IS knocked over, I don't have a whole cup worth of liquid everywhere, just a small spill (usually it's milk in the am and bedside ice water at night - they do act as a "thermos" too).
All day long, meals and out on the go my kids use "open cups". In the car, occasionally they will get one of those 'disposable' sippies or a straw cup. (I keep spare disposable kids cups in the passenger seat cup holder in the door...a nice back up!). We use them ALL THE TIME, at the movie theatre, playing at the park, etc. I can just buy ONE drink, without everyone having to share sips or fight over who holds it.
I hope this helps.