You will often hear misrepresentations and outlandish statements about Shia beliefs. I don't know why that is, just to spread hatred I guess.
Anyway, a lot of this is a bit overwhelming for the question you asked. I think Karina gave a great answer, and a good jumping off point for further research. I've included some helpful links.
BTW, many non-Muslims don't realize that Muslims (whether Sunni, Shia, or any other) believe in the resurrection of Jesus (as), and that he will walk with the Imam Mahdi (the Muslim Messiah, if you will) at the end time?
Now I need to defend against another answer.
1. They consider Hazrat Ali to be the Wali i.e. descendant, companion, associate, lord of Allah.
-- Untrue. The Shia consider Imam Ali (as) a descendant, companion and associate of the Prophet Mohammed (PBUH).
2. Shia worship Hazrat Ali R.A. and his decendents.
-- Untrue. The Shia revere Imam Ali (as) and the descendants of Prophet Mohammed. They are held in high-esteem. Prophet Mohammed (PBUH), his daughter Fatima Zahraa (as) and the Shia 12 Imam are considered models of virtue.
-- If this were true, then by the same mode of reasoning one could say that the Sunni worship Abu Bakr (as) and Aisha (as).
-- what proof? this is just a link to a forum index. Are we meant to read every forum post to findthis 'proof?'
3. Shias have legalized prostituion (Mutah)
-- Untrue. Mu'tah is a fixed-term marriage contract. Although it's true that some people abuse Mu'tah and liken it unto prostitution, that is not the way the practice is intended. There are always some in any group that have to ruin it for everyone.
4. Shias curse the companions of prophet Muhammad and his wives.
-- Perhaps some do, but Sunni state this over and over again. The worst I have ever heard a Shia say against anyone is "Astaqfirallah" (God forgive me) about Aisha (as). It is felt she made some poor choices during the course of the divide over the Caliphate/Imamate, but is respected for teaching others about Islam. Aisha (as), along with all of the wives of Prophet Muhammed (PBUH), are held in high esteem as the Mothers of the Believers.
-- With that said, Abu Bakr (as), Yazid and Uthman (as) are, it's true, extremely disliked for their machinations, ordering and carrying out the slaughter of the Prophet Mohammed's (PBUH) family, including his grandchildren.
5. Shias believe the Quran is incomplete and the real quran is with their 12th imam who is hiding in a cave.(lmaooo)
-- Untrue, and one of the craziest things I hear Sunni saying about Shia. According to the Shia, the 12th Imam is in occultation, meaning existing outside of time, before being resurrected at the end times. A Christian may understand this through Jesus (as), who is also in occultation until his resurrection. Jesus (as) is in occultation in heaven, whereas the 12th Imam, Imam Mahdi, is in occultation on earth, like the sun hidden behind the clouds.
-- The story spread by Sunni is a gross misrepresentation. The story is simply that the last place the Imam Mahdi was seen was, by some accounts, in his uncle's cellar or in a cave.
-- Imam Mahdi is not bringing "the real Quran" nor is the Holy Quran considered incomplete. The Holy Quran is considered perfected by Allah (SWT). Imam Mahdi will bring further texts that will help enlighten the Quran, and he will draw forth all of the religious texts.
*ETA: OK I've only been taught about the perfection of the Holy Quran and know nothing about the above mentioned missing parts eaten by a goat. I'm not a scholar of Islam, just a Comparative Religion major and teacher :)