Many people will say "Yes, of course, there's verses in the Qur'an that state exactly so! And of course, there's the common known rule that any verse is abrogated by a verse revealed chronologically later!"
Simply put, the "fact" that a peaceful verse is abrogated by a later verse about is simply not true. It was not taught in the Prophet's (peace be upon him) time and there is no sound scripture or hadith (sayings of the Prophet pbuh) to back up this claim. There are Muslims that teach this in order to lead those they want to do as they wish. This is where someone reading and learning for themselves is extremely important.
The verses that people use to back up their argument that Islam is a violent religion should be understood in their context. Not only in their scriptural context but also the situational context. We have documentation that states when and how verses were revealed. That means there is a place and time for each verse to be understood correctly. The most seemingly violent verses in the Qur'an should be understood in the time they were revealed... times of war. They were being actively attacked, even after moving to another city to find peace, and Allah (God) has never told His people to not stand up for themselves. As a Muslim, I understand these verses to mean that if someone is charging at my door to kill me, I should protect myself and my family.
Let's treat this fairly... there are verses in the Bible that I could use to prove it is a violent religion as well. Heck, especially if I never read the whole thing and relied on people to filter it for me, I could absolutely find verses to support this argument. Such as:
Matthew 10:33-35 (King James Version)
But whosoever shall deny me before men, him will I also deny before my Father which is in heaven. Think not that I am come to send peace on earth: I came not to send peace, but a sword. For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law.
But the fact is, as Americans, we are given the right and the freedom to read whatever books we want and therefore, we don't need to rely on people to tell us what is in a book... we can read it ourselves. So instead of coming to conclusions based on what other people say, let's make our own conclusions based on independent study and research.
For those still insistent on leaving it to others to find information for them, here's some verses from the Qur'an that touches on key points that many people either don't know, or ignore when they hear/read it:
Qur'an, Surah Al-Anaam (6)
151. Say: "Come I will rehearse what Allah hath (really) prohibited you from": join not anything with Him; Be good to your parents: kill not your children on a plea of want;― provide sustenance for you and for them;― come not nigh to shameful deeds, whether open or secret; take not life, which Allah hath made sacred, except by way of justice and law: thus doth He command you, that ye may learn wisdom.
152. And come not nigh to the orphan's property, except to improve it, until he attain the age of full strength; give measure and weight with (full) justice;― no burden do We place on any soul, but that which it can bear;― whenever ye speak, speak justly, even if a near relative is concerned; and fulfil the Covenant of Allah: thus doth He command you, that ye may remember.
153. Verily, this is My Way leading straight: follow it: follow not (other) paths: they will scatter you about from His path: thus doth He command you, that ye may be righteous.
154. Moreover, We gave Moses the Book, completing (Our favour) to those who would do right, and explaining all things in detail,― and a guide and a mercy, that they might believe in the meeting with their Lord.
155. And this is a Book which We have revealed as a blessing: so follow it and be righteous, that ye may receive mercy: