About your examples, 切符をください and 切符をお願いします, both can be used and understood that you want the ticket or you want to buy it. Another example, like if you want to order a cup of coffee in the cafeteria, you can say both, コーヒーをください and コーヒーをお願いします. However, when you want someone to buy coffee for you, I would say コーヒーを買って来てください。お願いします。The combination of these two phrases「～してください。お願いします。」is used very often. Please remember that it isn't the only way to request something. It depends on the person whom you ask something to and on the relationship between you and "someone". I hope this was helpful.

When you want to request or ask for something would you say? 切符をお願いします or 切符をください。

Could you give us any example situations?