Perhaps surprisingly, this is one of the questions I have been asked the most in my years as a pastor. People want to know if cremation is an acceptable practice for Christians to consider.
I'll start by saying that I've heard a number of very poor "Christian" arguments against cremation. Let me quickly critique 3 such arguments:
#1 Some people say that Christians should utilize bodily burial because that's what we find as the 'norm' in the Bible. This is the mistake of assuming that the Bible approves of everything it records. Yes, in biblical culture, it seems they tended to bury dead bodies (or placed them in tombs). So what? Are there identifiable biblical commands that say we must share that cultural practice?
#2 Others say that cremation should not be considered because it destroys the body, which the Bible says is the temple of the Holy Spirit. Think this through. The Holy Spirit does indeed dwell in the body of a believer while they are living, but there's no reason to believe that continues to be the case after death (and even if that was the case, is a decaying body a better home for the Spirit?).
#3 I've also heard people say that bodily burial fits better (symbolically) with the Christian belief in resurrection. I would grant that point. Bodily burial does better symbolize future resurrection than cremation. But the presence of 'symbolic' value doesn't determine whether something is mandatory or not for Christians. We are free to utilize that particular symbol or not (since it isn't commanded).
Not only do common objections to cremation fail to stand up to scrutiny, but it also seems a strong 'Christian' case could be made in favor of considering cremation. Consider the issue of stewardship. Cremation uses up far less God-given resources (money, space, etc.). It only speeds up the inevitable (we all return to dust anyways). And it's not like our all-powerful God is going to have a harder time resurrecting ashes than resurrecting a bunch of bones.
It seems to me that both bodily burial and cremation are legitimate options for a Christian to consider. There are pros and cons for each (beyond what I was able to cover here). Each person should be free to weigh those pros and cons thoughtfully and prayerfully.