The best thing to do with a bad zipper on a backpack would be to stop wearing a backpack because chances are you don't need the fucking thing in the first place since you took the process of the whole backpack being part of the culture a bit too literally.
Most backpackers don't ever go anywhere that an actual backpack would truly be necessary and would be better of with a rolling suitcase that probably costs 1/4 the amount of a backpack anyway. Seriously, why are backpacks so friggin expensive? They are made out of shoddier materials than rolling suitcases in the first place and they don't even have the decency to have wheels.
Ok, before i get to angry about the fact that most backpackers don't in fact need backpacks I'll instead look at something else.
find and remove the obstruction
First off, the main thing you need to look for is what caused the stuck zipper in the first place. This is often a piece of clothing or in the case of shitey backpacks, actually part of the backpack itself
Whatever you do, do NOT try to brute force your way though this because zippers, while being wonderful contraptions are very unforgiving once broken so since you are probably on some sort of stupid hippie journey anyway with your backpack, remember to just meditate and be at peace with the zip.
put some Vaseline on it
src
Vaseline is the cure for a lot of things and I i didn't believe it until i actually tried it myself but i'll be damned, it actually friggin works. On several occasions in the past just rubbing some Vaseline on a zipper resulted in it magically coming back to life. I have no idea why this works but it does.
Find someone to mend it
Backpacking is losing a lot of its appeal that it had in the past but something that still exists is the fact the completely replacing a zipper can sometimes be cheaper, easier, and less of a headache than trying to fuck with the damn thing every time you use it. Zipper technology hasn't changed in like 80 years so basically everyone knows how to work on it and it will cost next to nothing to get it repaired.
Admit that you aren't a real backpacker and get a suitcase
src
These are harsh words i know, but something that needs to be said to most of the people that I have seen with backpacks on for the past 15 years or so. I think the world just needs to start being more honest. If you are going from Mexico City, to Cancun, to Bogota, to some place on a beach in Costa Rica, I hate to point it out to you, but you are not a backpacker. You are a budget traveler and your backpack just makes you look like a dill-hole.
Fixing zippers on a suitcase aren't any easier than they are on backpacks... but they tend to be better quality and there will only be one or two of them.