1. The Happily Ever After
This is the typical Disney fairy tale ending where the good guys rejoice, the bad guys are upset and may or may not be punished. But bad guys are always out of the picture by the end of these, and then all of the good characters have not only solved the main problem, but every other problem is solved in the process. Anti-heroes or people who were bad and turned good also have happy endings. This is usually found in children's stories and chick flicks, and I personally have no problem with it as long as it is done properly.
Example 1: Disney's Snow White. The step mother dies, Prince Charming finds Snow White and presumably marries her and grants royal protection for the dwarves' mining industry. The wild animals are happy that no one will be asking them to clean house for them again.
Example 2: Confessions of a Shopaholic. Girl and guy get together, they get married, they live happily ever after and she has the kind of job she wants and is no longer in debt. She even gets her green scarf back.
2. The Realistic Happy Ending
This one is not quite as happy as the first. In this one, something may be lost, however, the goals of the main character(s) are still carried out in full, and everyone is left content with the ending nonetheless. This is a more adult ending than the first, and usually used more when guy movies need a happy ending. Some romantic stories may have this, but not comedies. Sometimes a children's story might have it if it dares. Action and Science fiction may go more for this style to add a certain level of depth. This is the type of ending that seems sad until you think about it from the character's points of view, and you realize everyone is actually happy.
Example 1: The Notebook. The old couple dies, but they're happy and she remembers before she dies.
Example 2: The Lion King. Mufasa definitely died and is no longer around, and the land is dead, but now Simba is in power and can fix it. Scar is dead.
3. The Bittersweet Ending
Obviously sad things happen here, but no one is entirely happy in the end. They achieve the goal, but they lose important things in the process. This is a more realistic version of a tragedy. Personally, I don't think anyone's life ends up that bad unless you haven't finished the story. But in a bittersweet ending, while the main character may die, or lose something invaluable like a lover, they finish what they intended no matter the cost. A lot of the deeper, more meaningful stories end like this.
Example 1: The Matrix. Neo dies, but the world is saved.
Example 2: The Bible. God gets beaten while living as a human. He loses a lot of people he loves. Lots of traitors, lots of greed, lots of murder, lots of hunger etc. In the end still, he ends up with the people who love him back and his goal is achieved. Humans are brought back to him and now we understand what it means to love. Or at least a hint.
Example 3: Death Note. Light dies and it makes one sad, but at least the world is saved (considering Light was a bad person, despite being the main character)
Example 4: Code Geass. Lelouch pretends to be an evil dictator so everyone will be united against him, then has Suzaku, his best friend come and kill him as a masked hero, so everyone would be united with him. So Lelouch dies, but he saves Japan and Brittania so they get along.
4. The Tragic Ending
In this, everything is lost. Perhaps people die or perhaps they don't. It doesn't matter. The goal is not achieved and never can be. The good guys have lost everything. Its possible the bad guys have also. Everyone learned a lesson but everything is lost so it doesn't even matter.
Example 1: Planet of the Apes. Nuff said.
Example 2: I honestly can't think of another depressing movie because I don't watch them very often!