The foundational prayer of our movement by Srila Prabhupada is to become a puppet in the hands of the Lord. When we take credit for what we do our strings are cut.
If there is some earthquake or there is some danger, naturally, spontaneously, we pray but we forget it. The tendency of offering prayer to the Lord at the time of danger is automatic. So we should know that we are in danger. We are in this material condition of life means we are in danger. Therefore, we should pray.
No conscious prayers go in vain. They are transmitted positively. Any prayer you offer to your Spiritual Master and Spiritual Master is conveyed to Krishna. No sincere prayers go in vain.
Remembrance and Prayers also can give us the desired result if they are properly done under expert guidance.
Prayer is a very important activity we have, it is a private talk between the devotee and the Lord. Akrura simply attained perfection by praying. In skanda-purana the glories of prayers is mentioned "A devotees whose tongue are decorated always with prayers is greatly respected even by saintly persons and such devotees are worship-able by demigods." It also helps us to establish our personal relationship with Krishna. because we are praying to Him, as that is our communication with the Lord.
We should pray that we become a sincere and bonafide student.