You’ve joined the rebellion, but why? Here are some examples of grievances against the Empire which lead to you joining the Rebellion. Kicking off a Star Wars Rebellion era campaign? Have this list on hand to help give players ideas for their backstory.

1. My business was shut down because someone on my list of clients potentially had Rebel leanings. Why not go all in?
2. I’m the child of a Senator. Once the Galactic Senate was dissolved, my father became an outcast. And so did I.
3. Some crazy old man told people I was a Jedi (I’m not I swear, I can’t even lift a spoon with my mind and my luck a cards isn’t that good) but someone told the local Imperial commander and I barely got out alive.
4. Our taxes keep going up, every cycle. Law and order is great but these taxes are killing the system’s economy. We’ve tried complaining to the Grand Moff but he just ignored us with some brusque hand waving. Now they’re telling us about upcoming wage and price freezes? Rationing dura steel? What’s next?
5. We run the largest turbo lift factory platform in the Rim. We can’t afford to keep bribing the military for looking the other way.
6. Some of my neighbors asked a question at the planetary governor’s speech . . . just asked a question. The next day, they were gone, and their were Stormtroopers guarding their door. How long before they come for me, for all of us?
7. I used to work at the Imperial military medical complex in the capital. One day, I got lost and wandered into the restricted wing. Those machines, those droids, what they were doing to those people . . . it wasn’t research, it was torture. I was lucky enough to leave without anyone noticing me, but the galaxy has to hear about this.
8. Getting into the Academy was hard, but I made it. Studied hard, maybe not top of the class but no slacker either. But some of the things we heard, stories about action in the Outer Rim and even in some core systems… I could tell I wasn’t the only one left with a bad taste… Some of us started getting together in groups, just socializing initially. I don’t know who was the first to begin, but one day I helped a fellow student hiding a memory chip. Moments later he was being escorted to the head master’s office. We were later told he dropped out of school. They got that thing right. From a shuttle at a height of 3000 meters. Apparently his back rockets didn’t fire. Terrible tragedy. A fine student. Condolences to his parents. I smuggled myself out the next day. For once got really lucky and came into contact with the right people, gave them the memory chip. Was invited to stay. Never looked back. This is the right thing to do.
9. That’s the second and the last time I’ve been cheated by an Imperial officer. First one might just have been a bad shlaaka worm in the brood. The next was a clear sign the the Empire is going to continually change whatever deal you make with them. To the Hells of Uuluph with them. They should have known better. The Rebels might be a bunch of self-righteous goody two-shoes, but they are my ticket to paying back the Empire until we’re even. And then some. Because nobody messes with [colorful name of PC].
10. The Empire was anxious to mine Thoralide to use in making Star Destroyers. So anxious that they didn’t mind flagrant safety violations and forced overtime which led to the death of numerous miners. My best friend died in the Thoralide mines on Cynda.  I joined the Rebellion after that. (See http://starwars.wikia.com/wiki/Thorilide/Canon).
11. The Empire is a gigantic bureaucracy. You were an Imperial employee, and you got swept under the carpet – no pay, no benefits, nothing. Reaching out to your superiors ended up in a death threat.
    I didn’t join the rebellion, the Empire handed me to them. When a sector patrol came to my small community, one that wasn’t involved with any galactic government, they accused us of harboring rebels. They trumped up charges on a local shop owner to justify it, saying he cheated the patrol’s commander. After that, they bombarded our community from orbit. A few of us survived, and after a few months were visited by regular traders, who gave us, half starved and nearly dead from exposure, passage off planet. That is why I’m fighting the Empire, they hit first.
12. Probably I would have just gone on my way except that the damn censors reduced the number of operas we could perform to, ugh, I don’t know, maybe three…. and all of them were terrible. Absolutely TERRIBLE don’t you know. And to add insult to injury when I mentioned to someone I might join the Rebellion the bastards seized my ENTIRE WINE CELLAR, other than this bottle here, which of course, I am happy to share with you, my being-in-arms.
13. An attempt to be cool by joining a student protest against imperial oppression got out of hand. Now you’re an outlaw, when all you really wanted was to study Literary Analysis and impress girls with how politically activated you were.
14. Worked for Coruscant Security Force before the formation Imperial Security Bureau and was Purged as undesirable along with most of the other Non-human officers and staff. The choice to join the Rebellion came when later he and the rest of his non-human neighbors were corralled into sectors designated Alien. And was required to have a workpass or a pass just to visit placed he’d frequented his entire life.
15. The Hutts have a bounty on your head. The Empire has a bounty on your head. The Rebellion is the best place to hide.
16. Member of a religious sect which promotes hermitage as a means of devotion. Left for a remote and primitive planet 20 years ago. Returned to find the Empire in control. The difference was enough of a culture shock to push you to action.
17. Well shucks, after the revenuers closed down our still there really weren’t nothin to do BUT weld a blaster to the roof of my speeder truck and jump it off things while firin it in the air and hollerin and throwin empties out the side. What’d they expect? Anyway that’s how me and all my cousins became the rebel alliance. Some people from another planet said they’d get us bigger guns to fight the revenuers but I can’t rightly say if I can fit a bigger gun up on my ole truck…
18. Why did I join the Rebel Alliance? I was born into it. My father was an officer in the Republic Navy and left the Empire a few months after its founding. My mother was in the Alderaanian service and was already unhappy with all of the civil liberties that Palpatine’s administration had eroded away. They both joined the Alderaanian Resistance led by Prince Organa and met each other. A couple of months after the destruction of the Sarlacc Project, here I come.
19. I was born on a freighter and rarely had the chance to step onto a planet. My parents were bonded pilots and were making a pretty good living by transporting goods and people for the Empire — items of low importance like medical supplies, food, the occasional groups of soldiers. Rebel agents were following an Imperial soldier on what was just another run to some far-flung sector. The Rebel Alliance intercepted Devarn’s ship and confiscated the soldier and goods. When they arrived at the Imperial outpost and informed the Commander of what happened, they were met by an Imperial Intelligence agent. They were asked to continue what they were doing and would be paid well to become informants.
20. I used to make a fortune smuggling spice along the Rim. The baronial patrolmen were delightfully inept and cheerfully corrupt. Suddenly the Empire moves in with their military governors and clone troops, and boom half my business gone. Unless you’re a Hutt you can’t make a dishonest living anymore. Now I run weapons to the Rebellion. It’s nowhere near as profitable, but if they overthrow the Empire I can make a new fortune off the resulting confusion.

Edited and compiled from the amazing crowd-sourced wisdom of the Google+ communities here and here.

What story justifications are there to have non-movie character Jedi during the Rebellion years?

The Jedi are incredibly rare at during this period of Star Wars history. The remaining ones would have escaped order 66 somehow, or they would not have had clones with them, or they did not take part in the clone wars. Force sensitives will have a very hard times finding those capable of teaching. If their abilities manifest in a public manner, they risk running afoul of the inquisition.

But…some of your players want to play a Jedi. No problem. Here are some reason why the Jedi exists in the Age of Rebellion:

1. A Jedi escaped Order 66 as a Youngling from the Jedi Academy and has been on the run ever since.
2. A young person is force sensitive and could be groomed as a Jedi, but requires a master to train them.
3. A youth had a vision from the Force called them to the path of the Jedi.
4. An experienced Jedi went beyond the Empire’s boundaries and has returned.
5. An experienced Jedi went beyond the Empire’s boundaries and has trained apprentices who have returned.
6. A Jedi was held in stasis for all these years and has been released.
7. The Jedi is part of a secret Jedi organization exists within the Empire that Obi Wan and Yoda kept secret or did not know about.
8. A Jedi who left the order prior to Order 66 and records of the Jedi were lost or deleted.
9. The Jedi was thought dead when their star fighter spun out into space but instead had survived.
10. The Jedi was thought dead but had enter a meditative hibernation for years due to extreme condition on a mission that went bad.
11. The Jedi scout was far away from the action of war at the time of Order 66, looking into rumors of ancient Jedi and Sith temples, and escaped execution.
12. The person was a Padawan who did not continue with the Academy and has lived off the grid on a backwater planet.
13. The Jedi was being held hostage by a crime syndicate during Order 66 but later escaped.
14. The Jedi quit the order in order to marry and created new identity to cover their past.
15. A non-Jedi force sensitive found a Jedi holocron and manages to train themselves with it.
16. A non-Jedi force sensitive person grew up on a little known fringe world and later met a Jedi who began mentoring them.
17. A Jedi injured in the closing days of the Clone Wars was in a Bacta tube on a medical frigate when Order 66 was sent out. Friends of the Jedimanaged to keep the few Clones from killing the helpless Jedi.
18. The Jedi was battling non-droid Separatist troops and found a sudden allies in the Separatists when the clones attempted to assassinate the Jedi.
19. A failed Jedi had left the Order and was bitter, angry, and awash in drink to dull the pain of the Clone Wars and lost in the obscurity of the Outer Rim before Order 66 went out.
20. The Jedi was a member of The Jedi Service Corps run by the Jedi Order. The members of the Service Corps were all considered Jedi, though many of its members had failed to pass their Initiate Trials and therefore could not proceed in training at the Jedi academy. While many of the Service Corps were killed during Order 66, many more were rounded up and taken to Byss by the Sith Lord-turned-Emperor for conversion training. This Jediis a fugitive who escaped their torture on Byss.
21. The Jedi was flying a Hyperspace-capable fighter or shuttle when Order 66 happened while most of the Clones were flying non-Hyperspace capable ships. The Jedi made it to their hyperdrive ring and escaped into hyperspace.
22. A Jedi captured by a criminal syndicate and frozen in carbonite is unfrozen years later.
23. A heretic kicked out of the Jedi Order before Order 66, for espousing some fundamental doctrinal change such as like “There’s no such thing as the Light Side or Dark Side; it’s all just The Force” or “There are two different Forces; The Light Side is not connected to The Dark Side.”
24. This person was kicked out of the Jedi Order before Order 66 for refusing the orders of an elder Jedi.
25. A Jedi was working undercover behind enemy lines at the time order 66 goes through, saw what was going on and kept under-cover until recently.

Based on my own ideas and crowd-sourced wisdom from the Google+ Community.

Also related — what was the Jedi doing to remain undetected? See this great Jedi Undercover Vocation list.