I Cor. 9 is an important passage that establishes the apostolic right of support. Paul gives a clear argumentation based on several different principles. What also must be clear is that an apostle was not required to enforce that right on the churches.
I Cor 9:1-18 Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord? are not ye my work in the Lord? If I be not an apostle unto others, yet doubtless I am to you: for the seal of mine apostleship are ye in the Lord. Mine answer to them that do examine me is this, Have we not power to eat and to drink? Have we not power to lead about a sister, a wife, as well as other apostles, and as the brethren of the Lord, and Cephas? Or I only and Barnabas, have not we power to forbear working? Who goeth a warfare any time at his own charges? who planteth a vineyard, and eateth not of the fruit thereof? or who feedeth a flock, and eateth not of the milk of the flock? Say I these things as a man? or saith not the law the same also? For it is written in the law of Moses, Thou shalt not muzzle the mouth of the ox that treadeth out the corn. Doth God take care for oxen? Or saith he it altogether for our sakes? For our sakes, no doubt, this is written: that he that ploweth should plow in hope; and that he that thresheth in hope should be partaker of his hope. If we have sown unto you spiritual things, is it a great thing if we shall reap your carnal things? If others be partakers of this power over you, are not we rather? Nevertheless we have not used this power; but suffer all things, lest we should hinder the gospel of Christ. Do ye not know that they which minister about holy things live of the things of the temple? and they which wait at the altar are partakers with the altar? Even so hath the Lord ordained that they which preach the gospel should live of the gospel. But I have used none of these things: neither have I written these things, that it should be so done unto me: for it were better for me to die, than that any man should make my glorying void. For though I preach the gospel, I have nothing to glory of: for necessity is laid upon me; yea, woe is unto me, if I preach not the gospel! For if I do this thing willingly, I have a reward: but if against my will, a dispensation of the gospel is committed unto me. What is my reward then? Verily that, when I preach the gospel, I may make the gospel of Christ without charge, that I abuse not my power in the gospel.
It is well also to understand this passage in context (esp. chapters 8-10) of Paul's argument of placing one's rights below or in subordination to the furtherance of the gospel. As Paul instructs the Corinthians to do so, he gives a specific example showing that he is not asking them to do something he has not done or is unwilling to do; something they very well knew he had done - serve them without charge. He clearly formulates his "right" in order to show that he had not insisted on it.
Also worthy of note is that Paul was not the only one for whom this was the common practice. He cites Barnabas* in verse six. In I Corinthians 12, he indicates that Titus also followed him in this.
II Cor. 12:13-18 For what is it wherein ye were inferior to other churches, except it be that I myself was not burdensome to you? forgive me this wrong. Behold, the third time I am ready to come to you; and I will not be burdensome to you: for I seek not yours, but you: for the children ought not to lay up for the parents, but the parents for the children. And I will very gladly spend and be spent for you; though the more abundantly I love you, the less I be loved. But be it so, I did not burden you: nevertheless, being crafty, I caught you with guile. Did I make a gain of you by any of them whom I sent unto you? I desired Titus, and with him I sent a brother. Did Titus make a gain of you? walked we not in the same spirit? walked we not in the same steps?
And though in I Cor. 9 Paul indicates that Peter and others did accept their maintenance (and even their wives, 9:5), it does not follow that they always did so. I Cor. 4 indicates that other apostles at one time or another labored with their hands. Note that "we" is the subject of the sentence in verse 12, and "apostles" is the antecedent of "we".
I Cor 4:9-12 For I think that God hath set forth us the apostles last, as it were appointed to death: for we are made a spectacle unto the world, and to angels, and to men. We are fools for Christ's sake, but ye are wise in Christ; we are weak, but ye are strong; ye are honourable, but we are despised. Even unto this present hour we both hunger, and thirst, and are naked, and are buffeted, and have no certain dwellingplace; And labour, working with our own hands: being reviled, we bless; being persecuted, we suffer it:
* Side note - to me it appears this reference to Barnabas even after he and Paul had separated (cf. Acts 15:36-41 & 18:1-17)