Worth telling to whom? Forget about everyone else, let's begin with yourself. What makes a story worth telling *to you*? And to move out of ad hominem land, let's change it to what makes a story worth telling to me.
That's a tough one (at least it is to me) because I don't know ahead of time what's going to be worth my while. Indeed, some of the stories I find most memorable (I guess that is an important element to "worth telling") are ones I encountered by accident, or ones where I came in not expecting much.
I know there are some stories that have changed people's lives. That's a pretty high bar. If I aimed for that, I doubt I'd ever write a story. But there have been many stories where I was struck by an idea, moved by a scene or character, or just plain loved the prose. Those are the three biggies for me as a reader. I see you included the word "exciting" and that would certainly qualify. I don't remember many characters in literature I would call exciting. Some movie characters might make the cut, but even then it's really the story that was exciting more than the characters themselves.
Anyways. As an author, I don't try for any of that. My first and most fundamental aim is to make a story that is complete. Close behind and in no particular order, come these.
Write a story that is clear and consistent. It can't have big plot holes or similar weaknesses. It must cohere.
Write prose that is the best I can manage. A whole raft full of secondary considerations enter here.
Write characters I find interesting. I don't have a formula for this. I start writing. I try to give the main characters a voice, but that can take quite a long time. I try to give them a background that adds interest and challenge. This, too, is highly malleable and takes time.
Pacing matters. This is a devil that rides my shoulders from first to last.
All of which requires something that is perhaps the hardest of all: I need faith in the story and in myself.
With every story I've written--five novels, four short stories--I have despaired. I've thought there were insoluble problems with the plot, pacing that dragged hopelessly, characters dull or inconsistent or both. I'm sort of ok with my prose, but that consistency business raises its head there, too. And with every story I've written, this has got so bad that I've come to a full stop. Unable to do more, not because I can't write more but because I've lost heart to write more.
This is where my first story comes to my rescue. It's not an especially good story. I don't even try to sell it; it's a freebie. But I finished it. It's a completed work. So when I'm in the Slough of Despond, I recall that work--and now, the other completed works--and remember not just that I can finish a story but how it *feels* to finish a story. So far, I've managed to pick myself back up and keep working.
None of which goes a whit toward your goal of memorable and exciting. Well, memorable and exciting ain't up to me, it's up to the reader to judge that. So I let that go. From my own work I don't get memorable or exciting, I get satisfaction of having told the story. That has to be enough (because it surely is not sales!).
