What is the Christian perspective on competition, in sports or business? It would seem to me that the drive to be the best or #1 is not in line with humbling yourself and serving the body of Christ. Are there any biblical references to support this?
First of all, it goes without saying that Christians should strive to do the best possible job they can to in any legitimate environment, whether on the job, in the home, in the Church, etc. That is because it relationship with Jesus requires us to be honorable and faithful in ever respect in our walk in this world (cf. Eph.6:5-9; 1Pet.2:18-21):
Whatever you do, work at it with all your heart, as working for the Lord, not for men, since you know that you will receive and inheritance from the Lord as a reward. It is the Lord Christ that you are serving.
Colossians 3:23-24 NIV
But "competition" in the sense we mean it in contemporary English is a concept for which it is difficult to find exact parallels in the ancient world (and particularly in the Bible). To use a rough analogy, in the US we often say something is "a challenge" when we are really trying to put a positive spin on a negative development - the task at hand is more daunting than usual, but in our optimistic approach to things we try to look at the enjoyment and satisfaction that may be involved in solving a particularly difficult problem rather than at the mess we may be in. As far as I am aware, there is no comparable concept to "challenge" in this sense in other languages/cultures (not even in French, for example, where the root word for "challenge" comes from). That is not to say that other languages/cultures wouldn't understand what we are talking about once it is explained, but it does mean that we often take for granted that certain ideas or ways of looking at the world which are second-nature to us will of course be familiar to others as well. That is not the case in the modern world, and it is even a less reliable guide when looking at the ancient world.
In a somewhat similar way, there is no exactly equivalent vocabulary item in either ancient Greek or Hebrew, and no exact conceptual equivalent either for what we mean by "competition". One could go on at length about the mind-set over similar things in Greek and Roman societies, and it is clear that there was a cultural predisposition toward excellence (the Greek arete is the closest we can come to expressing this idea in a word). But even though the structure of Greek and Roman athletics, to use one of your points of comparison, allows for one "winner", the idea is still more focused upon the bestowing of excellence (or the proving of excellence already there) through the process of the games. When we speak of competition today, we generally have a "pull oneself up by one's bootstraps" approach in our "mythology" of athletics. That is to see, we tend to view such competition as a noble process whereby it is the one or ones with true heart who work the hardest and persevere when the going gets tough who win out (or should win out) in the end. This "noble" aspect to our idea of competition is one that is not unparalleled in scripture:
Don't you know that all the runners in the stadium run the race, but that only one receives the prize? Run in such a way so as to achieve what you are after. And again, everyone involved in competition (agonizomenos, i.e., participating in the agon or contest) exercises self-control in all respects. Those athletes go through such things so that they may receive a perishable crown of victory, but we do it to receive an imperishable one. So as I run this race of ours, I'm heading straight for the finish line; and as I box this bout of ours, I'm making every punch count. I'm "pummeling my body", one might say, bringing myself under strict control so that, after having preached [the gospel] to others, I might not myself be disqualified [from receiving the prize we all seek].
1st Corinthians 9:24-27
You have a good point with your observation, however, because there are significant differences between the biblical application of this drive to "do well" and what is to be found in secular society, both ancient and modern. In the example given by Paul above, the athletes are all striving for a single prize which only one of them can possibly receive (so that the efforts of the many are ipso facto wasted). Furthermore, the thing they are striving for is ultimately pointless as well, because like all things in this world of emptiness, it will soon turn to dust. In the Christian life, on the other hand, the prizes we win by running for Christ are eternal and will ever be wonderful, and, since there is no shortage of heavenly treasure, we are not excluding others by our positive achievements. Quite to the contrary, our rewards are achieved in large part after personal spiritual growth by assisting in the process of the spiritual growth of our brothers and sisters in Christ, so that far from "winning away" rewards from them, we win our rewards by helping them win theirs:
Now therefore, my beloved brothers, be steadfast and immovable, abounding in the work of the Lord at all times, for you know that our labor is not in vain in the Lord.
1st Corinthians 15:58
Reward motivation is thus a very important element in the advancing Christian life (see the link: Christian Rewards), but, as you suggest, while it does contain the "strive for excellence" element of what we sometimes mean by competition, it is not at all competitive in the sense of succeeding at the expense of other believers (just the opposite). Both sides of this equation are important. Just as it would be a horrendous mistake to assume, for example, that it is the relative "success of my church/ministry/etc." which is the measure by which God will judge my work (i.e., pulling in more bodies than other churches/ministries), so it is likewise incorrect to assume that since there is no believer to believer competition for something tangible here on earth that we are therefore supposed to relax and not be motivated to strive for excellence. Each of these misapplications of scripture has its own pitfalls. We should ever be lending our fellow believers a hand up, but not allow anyone "to pull us down" into a lukewarm approach to our service to the Lord (1Cor.15:33). We should set a zealous example, and we should be stirred by the godly zeal and good example of others (Heb.12:1).
The second important element in our modern competition "mythology" is that of the best winning out which, in business terms, is sometimes described as social Darwinism. This notion of the active striving and triumphing of the superior person is most closely mirrored in scripture by the Greek word eritheia and its cognates, a word group expressing the idea of "striving", "rivalry", "ambition" and "contentiousness". This is forbidden Christians both directly (2Cor.12:20; Gal.5:20; Jas.3:14-16) and indirectly (Rom.2:8; Phil.1:17):
Let nothing be done through strife (eritheia) or vainglory, but in lowliness of mind let each esteem others better than themselves.
Philippians 2:3 KJV
In the same epistle, Paul also says that he is pressing "toward the mark (i.e., the finish line on the race course; Gk. skopos) for the prize of the high calling of God in Jesus Christ" (Phil.3:14 KJV). The juxtaposition of the two passages makes it clear that it is not the effort in what we consider competition that is the problem - the effort should be there for believers who are "red hot" for Jesus Christ rather than lukewarm - but rather the problem is any selfishness which seeks advantage, attention, glory for oneself, and is not first and foremost concerned with the welfare and spiritual advance of one's fellow Christians. Since, as I say, it is precisely by helping one another that we achieve the rewards we seek, seeking gain of any kind for ourselves and to the detriment of our brothers and sisters while in this world is a fundamentally flawed and wrong-headed approach which will yield only "wood, hay and stubble" at the judgment seat of our Lord Jesus Christ (1Cor.3:10-15). It is in fact legitimate to "provoke" one another to love (Heb.12:3-4) and to acts of love (2Cor.9:2). What is wrong is to seek advantage for self (Phil.2:4). What is wrong is selfishness (1Cor.13:5). And that is the essence of the matter.
So perhaps we may say that the "spirit" of competition is a good thing when properly directed. If we are truly striving to do our best for Jesus Christ (applying the first aspect of this concept), then that will turn out for the benefit of our fellow Christians who are aided by our efforts for His Church. And if we are truly striving to be the best we can be for Jesus Christ (applying the second aspect of this concept), then we give a positive example for our brothers and sisters to follow (one that does not disadvantage them in any way):
And let us consider one another to provoke unto love and to good works.
Hebrews 10:24 KJV
This sort of example, seeing the strong race that others are running, is spiritually salutary in every way. Inordinate secular competition in economic terms is pointless in every way as not a few of the scriptures proclaim (please see the link: The Vanity of Life):
And I saw that all labor and achievement spring from man's envy of his neighbor. This too is meaningless, a chasing after the wind.
Ecclessiastes 4:4 NIV
And yet it is true that "as iron sharpens iron, so one man sharpens another" (Prov.27:17). When we run with the best, we become better runners. Only let our running not be in vain. Let us run on the right course, with the right fellow runners, toward the right goal, and for the right prize. As Christians, we must learn to turn that innate spirit of competitiveness toward good uses, looking forward to a good report of our running from our Lord on that day to come. May it not be said that we ran for ourselves, but for Him and His Church, and that we ran as hard and as well as we could.
Please also see:
The Judgment of the Church and Christian Rewards
Hamartiology: The Biblical Doctrine of Sin (BB 3B)
In Him who left us the supreme example that we should follow it, our Lord and Savior Jesus Christ.