How to make scrum meetings more effective/productive in Agile Methodology?

In Agile method of software development, the teams along with scrum master meet once in a day to understand what each team member is working on and are there any impediments. This meeting is called Scrum meeting/daily scrum meeting/daily stand up meeting or even morning meeting. It may not be appropriate to call this meeting as morning meeting since the teams meet a the time that all scrum team members are comfortable with. Its a mandatory meeting for all the team members. Some may join over the call, its totally accepted but need to attend this meeting. The meeting usually happens in front of the scrum or kanban board.

As an agile standard, the scrum meeting lasts for 15 minutes and may slightly vary based on the size of the scrum team. However the meeting is time boxed for defined time. This needs to be ensured by the scrum master. So, what important things can be discussed in a such a short time so that its useful for all the team members? well, there is a fixed agenda set by agile framework. Each team member needs to answer following 3 questions.

1. What user story I was working on yesterday?

2. What user story I'll be working on today?

3. Are there any road blocks/impediments doing the task?

Over the time, this may look boring for the teams, however, the teams need to understand the importance of this and may go little beyond this agenda to make it effective. Following are some benefits to get out of scrum meetings.

• Lets say a user story A is dependent on story B and both stories A & B needs completion because they both have higher business value. In the scrum meeting, when the member working story A says, he/she has completed it, then story B can be planned on the same day by another person.
• When a story is completed, the best person to verify the story can be decided. There are two states of the story before we claim a story is completed, 'resolved' state and 'verified' state. Usually the person who resolves the story will NOT be verifying it, but some other team members. Unit level testing is done by the person resolving the story but the other person verifies the story from broader perspective which includes thinking about the impacted areas if any. This is best practice if story is dealing with critical code change in a complex software. 
• When a team member says that there is an impediment, its escalated to appropriate personal to get the resolution so that the sprint goals are not affected.
• Some team members may be facing technical difficulties which they just mention at scrum meeting. "I've a difficulty doing this user story and I want to discuss it offline with concerned people" and the details of the issue are not discussed in this meeting. Offline, other team members can talk to the person facing the difficulty and try to help/resolve that. A way towards moving self organized teams.
• There can be scenario where in particular story requires help from another cross functional team and scrum master talks to team members and discuss those during scrum of scrum meetings where scrum masters of different teams meet together for team dependencies. This may rarely happen even though you've identified the external dependency during PSI planning.

Scrum meetings bring transparency on what's being done/what user stories are being worked on and gives a glimpse on how the sprint is going on to the scrum master. Several other discussions among the team members may happen throughout the day informally may be over the coffee though.