I am assuming that you are referring to the 2007 release of Beowulf directed by Robert Zemeckis. Therefore, my answer will be based upon this production.

There are many differences between the Beowulf movie and the epic text.

1. The epic text is written from a Christian perspective. The importance of Christianity is seen throughout the text. First, Hrothgar builds Heorot because he wishes to give glory to God:

It came to his mind to order his men to build a hall, a master mead-house far mightier than any seen by the sons of earth, and therein would he bestow to young and old all that the Lord should give him, save people's land and the lives of men.

In the movie, Hrothgar and his Danes are Pagan. When Unferth comes to Hrothgar to see if the Danes should pray to the new Christian Lord Hrothgar says no.

Therefore, the ideology of Pagan and Christian are alternated.

2. In the epic text, Grendel attacks Heorot because he, a descendant of Cain, has been exiled into darkness. He could not wage war upon God himself so he, instead, waged war upon God's followers.

On the kin of Cain did the sovereign God avenge the
slaughter of Abel; Cain gained nothing from this feud and was driven far from the sight of men for that slaughter. From him awoke all those dire breeds: ogres, elves, and phantoms that warred with God a lengthy while.

In the movie, Grendel cannot stand the sound of music and singing which emanates from the walls of Heorot.

3. Beowulf, in the epic text, upholds true heroic values and acts accordingly. He stands by the code held up by the Anglo-Saxon culture. Therefore, all of his behaviors spoke to the fact that he was a true hero.

In the movie, Beowulf does not uphold all of the characteristics of a true hero. Instead, he lies about the fact that he killed Grendel's mother and he has an adulterous relationship with his queen's handmaid.

4. Lastly, the dragon which attacks the Geats and Beowulf is simply a new foe which Beowulf must face in order to fulfill his desire to die being a hero. It is best stated by Beowulf as to why a true hero must die as a result of a hero's battle:

“Do not lament, wise sire! It seems better that each man avenge his friends than to mourn them to no end. Each of us must await the end of his path in this world, and he who can, should achieve renown before death! That is the best memorial when life is past and a warrior's days are recounted.

In the movie, Beowulf dies murdering the dragon. While this is true in the text, the dragon's relationship to him is very different. In the movie, the dragon is Beowulf's son-- born as a result of his affair with Grendel's mother. Given the dragon symbolizes his failure, Beowulf feels that he must end the life of his son, the dragon.

There are many differences in the movie, Beowulf, and the original poem.

For one, Hrothgar was not the father of Grendel.  There is never any mention of either Hrothgar or Beowulf ever being romantically involved or enticed to become the fathers of Grendel or the dragon which appear as the major threats in the poem.

Also, Grendel's mother is never described as covered in gold and looking like Angelina Jolie, either.  She and her son live in a horrid place, and they are both descended of Cain--the first murderer on earth.  This is an Anglo-Saxon piece of literature, so it is imperative that you understand that loyalty and valor are huge ideals of the society which are expected to be kept.  Murdering someone is bad enough, but to murder a member of your own family-- a brother-- is considered one of the greatest sins you could commit.  This is one reason given for the misery that Grendel and his mother suffer-- their ancestor Cain murdered his brother Abel.  For this crime, all the family is punished.

Hrothgar is not portrayed as a man who has many lovers aside from his wife.  For that matter, neither is Beowulf when he becomes King.  Both men are respected and considered honorable men who are faithful to their wives.  Perhaps this was not true for real-life Kings, but in the poem both men are portrayed as faithful and loyal--not only to their wives, but also to the men who have pledged their lives to these Kings.

Beowulf also does not stay in Hrothgar's town and marry his queen.  Once Beowulf has fulfilled his duty to Hrothgar (because the King had helped Beowulf's father in his time of need and Beowulf feels a sense of duty to come to Hrothgar's aide as a form of repayment) by killing both Grendel and Grendel's mother, Beowulf returns home where he lives to a ripe old age and becomes King himself.  It is here, rather than at Hrothgar's castle, that he fights the dragon creature.

The movie is enjoyable, but as with every film ever made of a great piece of literature, the directors take enormous leaps in creative license and ruin it for those of us who have actually read the original works.  Hope this helps!  Good Luck!