In addition to lonesomeday's excellent answer I would also like to cite the following Scriptures where both Paul and James indicated that others should offer intercessory prayer for either them or others.
All Scripture is quoted from the King James translation.
In the following instance we see Paul asking for their prayers, to aid him in his work for the Kingdom of God, and as most Protestants that I know feel it is good that we ask others to pray for us in as much as it helps us to fulfill further the Kingdom of God.
Rom 15:30 through 32 Now I beseech you, brethren, for the Lord Jesus Christ's sake, and for the love of the Spirit, that ye strive together with me in your prayers to God for me; That I may be delivered from them that do not believe in Judaea; and that my service which I have for Jerusalem may be accepted of the saints; That I may come unto you with joy by the will of God, and may with you be refreshed.
In the book of James we find that Church Elders are exhorted to pray for and anoint the sick, also we see that we are told to confess our faults to one another and have them pray for our redemption.
James 5:14 through 16 Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him. Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.
In the book of acts we find Peter's intercession for the widows of Joppa, to bring back Dorcas from the dead, through intercessory prayer.
Acts 9:39 and 40 Then Peter arose and went with them. When he was come, they brought him into the upper chamber: and all the widows stood by him weeping, and shewing the coats and garments which Dorcas made, while she was with them. But Peter put them all forth, and kneeled down, and prayed; and turning him to the body said, Tabitha, arise. And she opened her eyes: and when she saw Peter, she sat up.
I must, however, disagree with your statement about having anyone else pray for us; we consider to be dishonoring Jesus. Only in the asking for the forgiveness of our sins do we believe that we alone must pray directly to Jesus for forgiveness. Those sins belong exclusively to us, and for that we must ask Jesus to personally intercede with the Father. According to the following Scripture only Jesus can do that since he alone is the propitiation for our sins.
1st John 2:1 and 2 My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
For my part why should I pray to a dead Saint, when I have both a live Jesus as intercessor and Father God to whom Jesus said to pray directly in the Lords prayer.