When can I expect my child to take turns?

3 years. 3-y-o toddler is expected to share his/her toys, play well with another child, and take turns.
Parallel play. Toddlers typically play in parallel with other children. In other words, they are playing next to other children, but not really playing with them. Eventually, perhaps not until school age, children will start to play with each other, in a cooperative arrangement. Until they move past parallel play, don't expect them to take turns.