I'm going to do my top 10 :)
1- Titanic
You say you're not that knowledgeable when it comes to movie, but I'm pretty sure you have seen this movie or at least heard about it (I know some people who's never seen it), it's a must-seen. Basically a love story between a poor guy and a rich girl on the famous ship that *spoiler alert* sank ;)
What I love about it is everything, it's a classic movie, but I really do love everything about it. Even after the 15th time I still cry :P
(Honest) Trailer: http://www.youtube.com/watch?v=s6mMvBeEPT4
2- The Green Mile
It's an AMAZING movie about John Coffey, a man who is accused of raping and killing two little girls, and arrives on death row in a prison of Louisiana in the 1930's. However, he is shy, soft-spoken, and emotional, and he reveals extraordinary powers of healing.
It's a very emotional story and definitely a must-seen. The actors are amazing and their performances are breathtaking! I love Tom Hanks he's a great actor! The end also makes me cry.
Trailer: http://www.youtube.com/watch?v=ctRK-4Vt7dA
3- The Godfather trilogy (especially the first two)
You probably also know what it is about, basically: Italian Mafia. But it's definitely the best mafia movie ever!
Why I love it? Well, I love mafia movies and I have Italian origins :P And the actors are great!
Trailer: http://www.youtube.com/watch?v=sY1S34973zA
4- Fight Club
It's a bit complicated to explain haha, this is Imdb's summary: An insomniac office worker looking for a way to change his life crosses paths with a devil-may-care soap maker and they form an underground fight club that evolves into something much, much more...
I like it because the end makes the whole movie amazing! It's a bit complex at first but when you see it after you notice new things each times. I'm not a fan of Brad Pitt, but he and especially Edward Norton were great in it!
Trailer: http://www.youtube.com/watch?v=M8PRC3HbWqo
5- The Departed
Two men from opposite sides of the law are undercover within the Massachusetts State Police and the Irish mafia, but violence and bloodshed boil when discoveries are made, and the moles are dispatched to find out their enemy's identities.
I love it because it's from Martin Scorsese my favorite director, and Leonardo DiCaprio is one of my favorite actor, I won't qualify the movie as a must-seen though, it's just another great mafia story!
Trailer: http://www.youtube.com/watch?v=SGWvwjZ0eDc
6- The Prestige
This one is definitely a must-seen! It's about a rivalry between two magicians in the 19th century. They become ennemies after the wife of one of the magician's wife dies "accidentally" on the other magician's trick. They will try to sabotage each other and kill each other the whole movie (How lame my story sounds, but the movie is really great!).
Again, it's from Christopher Nolan, one of my favorite director, and Hgh Jackman and Christian Bale are two of my favorite actors, and they are brilliant in this movie!
Trailer: http://www.youtube.com/watch?v=o4gHCmTQDVI
7- Million Dollar Baby
Such a touching story about a woman who is determined to learn boxing, with a hardened trainer to become a professional. A strong relationship will be built between both of them until an unfortunate event happens :(
I love it because every character is touching, and the unfortunate event makes me angry every time.
And again, Clint Eastwood is one of my favorite actor/director and so is Morgan Freeman :P Defintely a must seen!
Trailer: http://www.youtube.com/watch?v=OCDZLsqwH28
8- The Pianist
Another sad movie, about a Jewish pianist in Europe who sruggles to survive during WWII. No need to add more to express how sad it is. Adrien Brody's performance was breathtaking!
Trailer: http://www.youtube.com/watch?v=CIRLLPa-j9o
9- The Notebook
It's one of my favorite Romantic movie. You probably already heard of it.
Trailer: http://www.youtube.com/watch?v=S3G3fILPQAU
10- The Shawshank Redemption.
I think it's considered as one of the greatest movie of all time, it has 9.3/10 on Imdb (most of the movies I mentioned had around 8.5/10 btw :) )
Here's the storyline: Andy Dufresne is a young and successful banker whose life changes drastically when he is convicted and sentenced to life imprisonment for the murder of his wife and her lover. Set in the 1940's, the film shows how Andy, with the help of his friend Red, the prison entrepreneur, turns out to be a most unconventional prisoner.
Trailer: http://www.youtube.com/watch?v=6hB3S9bIaco
I also would like to add the LOTR Trilogy, the Harry Potter series, the Dark Knight trilogy and the Star Wars series as well, I'm a huge fan :)