This is a relevant question, particularly since the original issue for guys was being lazy with what we were called to do (Adam in the garden). In seeing this laziness we desire to not be associated with being lazy and we get ambitious. We value passion in school. We value passion in work. We really value passion in sports, and other fields as well. Is this what we are called to? Ambition in school, work, and recreation? Or is this a bad thing? Or is it something else?
Let's look at a passage of scripture that deals with this issue. Keep in mind we will look at several passages, and I will not do enough justice for each one. I encourage you to read and study them yourselves to get a full picture of what God wants us to understand from His Word.
And James and John, the sons of Zebedee, came up to him and said to him, "Teacher, we want you to do for us whatever we ask of you." And he said to them, "What do you want me to do for you?" And they said to him, "Grant us to sit, one at your right hand and one at your left, in your glory." Jesus said to them, "You do not know what you are asking. Are you able to drink the cup that I drink, or to be baptized with the baptism with which I am baptized?" And they said to him, "We are able." And Jesus said to them, "The cup that I drink you will drink, and with the baptism with which I am baptized, you will be baptized, but to sit at my right hand or at my left is not mine to grant, but it is for those for whom it has been prepared." And when the ten heard it, they began to be indignant at James and John. And Jesus called them to him and said to them, "You know that those who are considered rulers of the Gentiles lord it over them, and their great ones exercise authority over them. But it shall not be so among you. But whoever would be first among you must be slave of all. For even the Son of Man came not to be served but to serve, and to give his life as a ransom for many." - Mark 10:35-45
What exactly is it that James and John want?
They want to be great in the kingdom of God. Mark doesn't indicate to us here that the brothers are even operating under evil intentions (knowingly) but that they are genuinely interested in being ambitious in this kingdom. As we can see from the discussion, however, though they are not intentionally pursuing a dangerous path, they are definitely missing out on a key understanding of the kingdom of God. They are desiring to be great in the kingdom of God, by means of the kingdom of the world. As addressed really well in a book by C.S. Lewis called The Great Divorce, you cannot have a little bit of hell with you in heaven (or New Creation). I would definitely say that James and John, from their perspective, are pursuing God in this question, but they are missing the point. Too often it is clear in the lives of Christians that in our language and thoughts, we are pursuing God, only to discover that we too are missing the point. We often think that being great in the kingdom of God means that we are speaking on the stage in a church. Or we are participating in a band in worshiping God through song. Or when our name is mentioned in some sort of missions bulletin. 2 Corinthians 5:15 states "and he died for all, that those who live might no longer live for themselves, but for him who for their sake died and was raised." Paul is painting the picture that through Christ's death on the cross and His purchase of His people, that we (if we are among His people) are by no means, to live FOR ourselves any longer. You can speak on a stage. You can participate in a band, or go on mission, but if it is about you then it is in vain that you do these things. God will most definitely even use the work of people who do His work for their own pride, but they will likely be preaching a gospel that they themselves might be missing out on. It is in pride and pride alone that we do our work to build up ourselves. Lets look at a passage that discusses the danger of pride.
Like snow in summer or rain in harvest,
so honor is not fitting for a fool.
Like a sparrow in its flitting, like a swallow in its flying,
a curse that is causeless does not alight.
A whip for the horse, a bridle for the donkey,
and a rod for the back of fools.
Answer not a fool according to his folly,
lest you be like him yourself.
Answer a fool according to his folly,
lest he be wise in his own eyes.
Whoever sends a message by the hand of a fool
cuts off his own feet and drinks violence.
Like a lame man's legs, which hang useless,
is a proverb in the mouth of fools.
Like one who binds the stone in the sling
is one who gives honor to a fool.
Like a thorn that goes up into the hand of a drunkard
is a proverb in the mouth of fools.
Like an archer who wounds everyone
is one who hires a passing fool or drunkard.
Like a dog that returns to his vomit
is a fool who repeats his folly.
Do you see a man who is wise in his own eyes?
There is more hope for a fool than for him. - Proverbs 26:1-12
This Proverb goes into detail about how bad it is to live foolishly. There is no honor for them, a rod for their backs, its dangerous to correct them because you could become like them, its dangerous to not correct them because they need the instruction, and on and on. We get this. We would hate the thought of being foolish. We strive very ambitiously to be considered wise. But verse 12 says something shocking, and indeed it is intended to do so. It states "Do you see a man who is wise in his own eyes? There is more hope for a fool than him." So rereading the Proverbs with this new information could go like so
"Honor is not fitting for the fool. Even less so for those who pride in themselves."
"Fools should be beat with a rod on their backs. Even more so for the backs of those who are wise in their own eyes."
"Arguing with a fool could make you like him. But beware of arguing with those full of pride. Becoming like them would bring you no hope."
"A proverb in the mouth of a fool is painful. It is truly dangerous in the mouth of the proud."
What does this passage teach us about our ambition being rooted in pride?
It clearly teaches us that ambition rooted in pride is at the very root of our sinful, broken nature. In fact it is at the very root of everything God hates. Psalm 5:5 states "The boastful shall not stand before your eyes; you hate all evildoers."
I won't go through all of it, but Matthew 25 in it's entirety helps us understand the nature of what it means to live out a correctly ambitious life. The first story (briefly summed up) teaches that we should be prepared for the arrival of our King like the wise virgins, and not like the foolish ones. But how? The second story tells us that we are to be prepared by using what God has given us to be fruitful in this life, like the wise servants in the story and not like the foolish one who buried his talent underground. But how are we to be fruitful? The third parable explains that we are to use what God has given us to be fruitful by lovingly pursuing people, like the sheep, as opposed to the goats.
Quickly summed up, we are to ambitiously be prepared for the Lord, by being fruitful with what God has given us, by eagerly serving people through service (to Christian and non-Christian) and through the proclamation of the gospel (to the Christian and the non-Christian).
Jesus in Matthew 6:33 states, "But seek first the kingdom of God and his righteousness, and all these things will be added to you." The problem is if you are quoting this, and doing kingdom work while focusing on these "other things" then you were never seeking the kingdom. Seeking first the kingdom means that you are pursuing Christ, knowing full well you may only ever get Christ (and His people), and that is all you need.
SO. Is ambition a good thing? Absolutely! Provided it is seeking His kingdom, by preparing the way of the Lord by being fruitful with what he has given you, by serving people, and proclaiming His Good News. If this isn't how you are ambitious, then you are missing the first step - die to you. Kneel to the King.