James and John make a request (through their mother)

Mark 10:35 And James and John, the sons of Zebedee, come unto him, saying, Master, we would that thou shouldest do for us whatsoever we shall desire. Matt 20:20 Then came to him the mother of Zebedee's children with her sons, worshipping him, and desiring a certain thing of him.
Mark 10:36 And he said unto them, What would ye that I should do for you? Matt 20:21a And he said unto her, What wilt thou?
Mark 10:37 They said unto him, Grant unto us that we may sit, one on thy right hand, and the other on thy left hand, in thy glory. Matt 20:21b She saith unto him, Grant that these my two sons may sit, the one on thy right hand, and the other on the left, in thy kingdom.
Mark 10:38 But Jesus said unto them, Ye know not what ye ask: can ye drink of the cup that I drink of? and be baptized with the baptism that I am baptized with? Matt 20:22a But Jesus answered and said [1], Ye know not what ye ask. Are ye able to drink of the cup that I shall drink of, and to be baptized with the baptism that I am baptized with?
Mark 10:39a And they said unto him, We can. Matt 20:22b They say unto him, We are able.
Mark 10:39b And Jesus said unto them, Ye shall indeed drink of the cup that I drink of; and with the baptism that I am baptized withal shall ye be baptized: 40 But to sit on my right hand and on my left hand is not mine to give; but it shall be given to them for whom it is prepared. Matt 20:23 And he saith unto them, Ye shall drink indeed of my cup, and be baptized with the baptism that I am baptized with: but to sit on my right hand, and on my left, is not mine to give, but it shall be given to them for whom it is prepared of my Father.
Mark 10:41 And when the ten heard it, they began to be much displeased with James and John. Matt 20:24 And when the ten heard it, they were moved with indignation against the two brethren. Luke 22:24 [2] And there was also a strife among them, which of them should be accounted the greatest [3].
Mark 10:42 But Jesus called them to him, and saith unto them, Ye know that they which are accounted to rule over the Gentiles exercise lordship over them; and their great ones exercise authority upon them. Matt 20:25 But Jesus called them unto him, and said, Ye know that the princes of the Gentiles exercise dominion over them, and they that are great exercise authority upon them. Luke 22:25 And he said unto them, The kings of the Gentiles exercise lordship over them; and they that exercise authority upon them are called benefactors.
Mark 10:43 But so shall it not be among you: but whosoever will be great among you, shall be your minister:44 And whosoever of you will be the chiefest, shall be servant of all. Matt 20:26 But it shall not be so among you: but whosoever will be great among you, let him be your minister; 27 And whosoever will be chief among you, let him be your servant: Luke 22:26 But ye shall not be so: but he that is greatest among you, let him be as the younger; and he that is chief, as he that doth serve.
Mark 10:45 For even the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many. Matt 20:28 Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many. Luke 22:27 For whether is greater, he that sitteth at meat, or he that serveth? is not he that sitteth at meat? but I am among you as he that serveth.
       

[1]Jesus is no longer talking to the woman but to her sons.

[2]Luke places this incident at the beginning of the last supper.

[3]See Mark 9:34-35 for a different occasion on which this question comes up.