Both of our kids had their bottles taken away on their first birthday. They didn't have an option but to use a sippy cup from that point on.
I was concerned about our son because he wouldn't take a sippy cup when we'd tried. When he didn't have a choice, he did great. We had to have a few different varieties around until we knew which he preferred.
Our daughter started around 9 months because the Day Care needed the spot in the infant room, and she needed to be off a bottle to transition. They used a cup during the day. She was off a bottle at 10.5 months.
I'd recommend stopping bottles as quickly as possible. They are old enough to use a cup. We even would give water, small amounts of milk in normal (not sippy) cups around a year so they understood how to hold and use a cup.
At 3.5 and 21 months, we still use sippy cups primarily out of concern for spills in most areas, but both will drink out of normal cups at the table with few accidents.
hope that helps!