I have heard some people speak against cremation for Christians, because of the ties it has to some eastern religions. But what does the Bible actually say about cremation, or any other burial practices?
There is nothing in the Bible that specifically deals with what to do with the bodies of the deceased. Cremation does not appear to be a part of any burial customs of God's people in biblical times.
Joseph (Jacob's son), in faith, gave instructions to the Israelites to carry his bones back to the Promised Land when God would give Israel that land centuries after he died. With his role in Egypt, he may have even been mummified according to Egyptian customs.
We also know that Jesus was not cremated, and His body did not see corruption.
It seems that the biggest issue with cremation is that it actively destroys the body rather than passively surrendering it to natural processes.
tl;dr - no.
While it is true that there is no explicit instruction given in scripture on whether cremation is acceptable or not; however, there are numerous positive examples of either burial or interrment being the normative practices in both Old and New Testaments. Further, some of these passages strongly imply that to die and be buried is superior to dying and not being buried:
[Judgement prounounced against Jeroboam] ... 9 You have done more evil than all who lived before you. You have made for yourself other gods, idols made of metal; you have aroused my anger and turned your back on me.
10 “‘Because of this, I am going to bring disaster on the house of Jeroboam. I will cut off from Jeroboam every last male in Israel—slave or free. I will burn up the house of Jeroboam as one burns dung, until it is all gone. 11 Dogs will eat those belonging to Jeroboam who die in the city, and the birds will feed on those who die in the country. The Lord has spoken!’
12 “As for you, go back home. When you set foot in your city, the boy will die. 13 All Israel will mourn for him and bury him. He is the only one belonging to Jeroboam who will be buried, because he is the only one in the house of Jeroboam in whom the Lord, the God of Israel, has found anything good... 1 Kings 14 NIV [emphasis added]
Additionally, there is one clear example in the scripture of the cremation of remains that is in an extremely negative (ie contra-indicated for normal circumstances) context:
...16 Then Josiah looked around, and when he saw the tombs that were there on the hillside, he had the bones removed from them and burned on the altar to defile it, in accordance with the word of the Lord proclaimed by the man of God who foretold these things.
17 The king asked, “What is that tombstone I see?”
The people of the city said, “It marks the tomb of the man of God who came from Judah and pronounced against the altar of Bethel the very things you have done to it.”
18 “Leave it alone,” he said. “Don’t let anyone disturb his bones.” So they spared his bones and those of the prophet who had come from Samaria.
19 Just as he had done at Bethel, Josiah removed all the shrines at the high places that the kings of Israel had built in the towns of Samaria and that had aroused the Lord’s anger. 20 Josiah slaughtered all the priests of those high places on the altars and burned human bones on them. Then he went back to Jerusalem... - 2 Kings 23 NIV
Just in case you missed it, Josiah's righteous rampage involved the defilement of altars on the "the high places" by cremating human remains on them. The remains of the prophets referred to in 1 Kings 13, while in close proximity to the defilement of the altar at Bethel, were ordered not to be "disturbed" in this way, rather they were "spared".
While it could be argued that these references occur in a particular cultural milieu and the underlying connotated pairings of (burial/interment,blessing/reward) and (scattered/devoured/cremated remains,cursing/judgment) make sense in that cultural context, but are no longer (or at least not as) applicable in modern cultural contexts; if we are purely focusing on what the bible says about this particular matter, it certainly doesn't provide any support for the idea of it being an "acceptable practice", on the contrary, it seems to be a contra-indicated practice.
The idea comes from the concept that whatever happens to our bodies in this life will impact our bodies for eternity:
Matthew 18:9 (NIV)
And if your eye causes you to stumble, gouge it out and throw it away. It is better for you to enter life with one eye than to have two eyes and be thrown into the fire of hell.
Here, Jesus clearly states that if we are blinded, we will be blinded once we enter heaven.
Cremate, if you want
The argument for cremation says that Jesus was probably using hyperbole when he said this, since other passages show that there will be no blindness in heaven:
Isaiah 35:5 (NIV)
Then will the eyes of the blind be opened and the ears of the deaf unstopped.
Also, even though this body is completely destroyed, we will be given an eternal one:
2 Corinthians 5:1
For we know that if the earthly tent we live in is destroyed, we have a building from God, an eternal house in heaven, not built by human hands.