A friend came up with a great example with Scully and Mulder, the two X-Files protagonists who disagreed ALL THE TIME.
Examples of well-crafted conflict? If it's on the bookstore shelves it's likely packed with well-crafted examples of conflict--and multiple examples per novel.
Conflict is everywhere in fiction and in real life.
First, it's worth it to define conflict.
In fiction, conflict is the thing that causes characters to act. And that's not always evil and it's not always overt. Conflict can be subtle. Conflict does not necessarily have to be a struggle or a fist fight. It can be as simple as the need to make a decision, the desire to make a decision, the failure to make a decision. In fact, a story's primary conflict isn't usually evil, even in a good vs. evil story. Evil happens all the time, but doesn't always cause people to act. For example, human trafficking is a real thing that happens every day in probably every nation of the world. But have you done something about it today? Ever? Has the presence of this evil caused you to act? Probably not. So the conflict in a good vs. evil story is the character's decision and why he makes it. Why does he choose to fight? Why does Steve Rogers choose to undergo those secret tests that turn him into Captain America? There's the real catalyst.
But what if someone you loved were caught up in human trafficking? Example: The film Taken, starring Liam Neeson. How much time had he spent battling human trafficking until his own daughter was kidnapped for just such a nefarious purpose?
Action happens when the evil personally impacts a character, inspiring or sometimes forcing a reluctant character to act.
But, as Stella pointed out, conflict isn't always about good vs. evil, and it isn't always so in-your-face.
To begin with, conflict can be divided into two neat little boxes: Internal Conflict and External Conflict.
Internal Conflict occurs within the character's mind or body. Self doubt or guilt, desire for change or inspiration. As you can see, not all internal conflicts will be negative, or good vs. evil. Sometimes it's as simple as wanting something more out of life. Maybe a decision that needs to be made. Maybe as simple as which color carpet to choose. Even the internal conflict that arises from an inability to make a decision. Internal conflicts can be considerably more subtle than external ones. Internal conflicts are also those that dig into the heart, that reach out to our sense of empathy.
External Conflict occurs outside the physical being of the character. Some event happens that causes the character to want to act or change, or forces the character into action. For example, a fire in your house would force you to act in order to save your life. Liam Neeson's character was forced into action by his love for his daughter. Millions of Americans were inspired to action by the events of World War II, growing victory gardens, women entering the workforce in huge numbers, out of a desire to help our boys overseas. Thousands of Europeans were inspired to act in the service of those around them--families hiding Jews or supporting resistance efforts.
One World War II example of both kinds of conflict (because while internal conflict can exist alone, external rarely can) can be found in Cori Ten Boom's autobiographical book, The Hiding Place. Ms. Ten Boom describes the internal struggle their family underwent as they were faced with the external reality of the suffering of their Jewish neighbors. They were inspired to act, to help, but only after their own internal struggle over the safety of their own family. In addition, much of the remainder of the book is Cori's internal struggle, her decision to not give in to despair despite the horrific external forces that were seeking to force her to do just that. As is clear in her narrative, sometimes the resolution to these conflicts occurs only in the heart and in the mind. In every way she appeared to be giving up, giving in, as she externally obeyed the commands of her captors. But internally she was conquering them and herself through the way she chose to think.
But I don't think Stella is asking for a lesson in the definition of conflict in fiction.
I suspect the real question is, "How do I identify conflict in a story?"
Because that is 3/4 of the battle. If you can clearly identify the catalyst that spurs your character to act, and secondarily, how that character resolves that problem (or fails to resolve the problem), your story is already written. Because that's what stories do.
Stella asked for examples. Here are several from Flash Fiction Online.
By way of exercise, read each story. Identify the catalyst that causes each character to act or change in some way--the conflict. Be careful. There may be more than one. Can you identify the main conflict, as opposed to secondary ones? Identify the result of that action, or the resolution. After the given links I'll give my take on A) the conflict or conflicts and B) their resolutions.
Irma Splinkbottom's Recipe for Cold Fusion (Flash Fiction Online, November 2009) I use this story a lot when giving examples of, well, pretty much anything. Mostly because I loved it then and I love it still.
Kolkata Sea (Flash Fiction Online, July 2010) Super subtle conflict here.
Irma Splinkbottom: The main conflict in this story is Irma's own self confidence. At the root of it, that's what causes her to act, that's what she is up against. She thinks she can do better than those know-it-all scientists, so she acts. With measuring cups and microwave. The story resolves itself in Irma succeeding externally, but learning an internal lesson in doing so. Of course, she did have to pay with her life.
Kolkata Sea: As I stated, the conflict is subtle in this story. What is it? What is the thing that causes the character to act? I would argue that it is love and longing. This story is less a character piece than it is a setting piece. It explores how the world might change in a globally warmer future. But it has characters who act within that tableau. Something has spurred them to do so. The mother wants to show her son her past. The son wants to honor his mother's longing for that long ago world by scattering her ashes over the submerged city--the resolution.
The Pony Spell: The conflict in this story is much more transparent--actually several conflicts. There is the 'good vs. evil' struggle between the wife and the witch that results in the witch acting (Which is good, which is evil?) by casting that spell, which immediately brings up conflicts within the family of what to do with the wife-pony and is the catalyst for the main conflict--that of what to do when the witch offers to change the wife back. There is the additional conflict of the witch's guilt at her actions, which is resolved when she offers to change her back. The final resolution is humorous: Husband decides to leave the wife as a pony and everyone is happy, except maybe the wife.
Peace-and-quiet Pancake: A couple of different points of conflict in this story. A story really rarely ever has just one. First is the conflict between the woman and her father--a tense relationship flipped upside down with the daughter becoming the caregiver. The second is the conflict within the woman at her observation of the father and child in the waiting room. What should she do? All her struggles and resolutions are internal. Nothing happens externally, she does very little externally, to change things within her environment. The changes, the decisions, are within herself. The resolution is in her coming to terms with her relationship with her father.
Honeybee: In Honeybee, the conflict is an external one that spurs the main character to action. The disappearance of the honeybee is the primary research objective for our character who, in the end, bends the rules to save them--resolution. Her decision to act is spurred on additionally by the internal conflicts caused by love and longing. Again, that love and longing. They're powerful conflict devices and used often. Really, we see them in the Pancake story and The Pony Spell in addition to this and Kolkata Sea.