Psalm 34:17 The righteous cries out and the Lord hears him...
The "righteous" does not mean someone who is perfected and free from sin but instead someone who has been redeemed by the Lord; a person loved by God and set apart for his purposes. When you are a child of God your prayers are heard by him. You can go to God on the behalf of others and know that you are heard. This brings great hope as we seek the Lord for the salvation and help of those who do not walk with him.
It blesses others:
Mark 2:5 And when Jesus saw their faith he said to the paralytic, "My son your sins are forgiven."
In this circumstance Jesus was preaching in a house and there was no more room in the house or even at the door. Some friends were bringing their paralyzed friend to see Jesus in hopes of healing. They had heard of the supernatural works Jesus was doing and they were sure if Jesus touched the man he would be healed. When they saw there was no room to get in, their faith motivated them to go to extreme lengths to get that man to Jesus. Not being halted by obstacles, they climbed the roof, dismantled it, and lowered the man down. They relentlessly brought this man to Jesus and because of their faith, it says, he was healed. Your faithfulness to bring others to Jesus in prayer can lead to their blessing.
It blesses you:
Job 42:10 And the Lord restored the fortunes of Job when he prayed for his friends.
Certainly Job's blessing was not dependent on his prayers for his friends but the scripture clearly makes the point that praying for others can result in blessings upon you. In this particular situation Job's "friends" were earlier described as "miserable comforters" (Job 16:2) and yet now he prays for them. Something happens in our disposition toward others when we begin to sincerely pray for them and often times it results in unexpected personal blessing. That blessing may be tangible or it may be the even greater blessing of a heart conformed more to love like Christ.
May these reasons motivate you to faithfully pray for others today...or even right now.