I'm 14 and of course I want snapchat. But my parents don't want me to have it. They just don't like the disappearing photos and that the texts don't save by default. I know myself and I know that I would NEVER send anything inappropriate and if I ever received anything inappropriate I would tell someone. I also want the app for my friends only and would never chat with a stranger. What is your opinion?

Your parents get to decide this, but what I will say is this (to you): present your case to them as though it's homework. Make a list of how you help around the house, what chores, what you are good at obeying, and what your grades are in school (the biggie, of course). You could also look online for some solid evidence of how little goes wrong on snapchat, and at what ages other kids are likely to start using it. You could also ask for 30 days of it as a trial run, and you'll show them how it works, and let them try it. End with how appreciative you are that they are your parents! (Who can resist the soft sell?)

They have the right to say that your promise is all very fine but not applicable, any more than I can tell the grocery store I'll come back later with money. (I tried that, and they even KNOW me there!)

Of course teens want their parents to trust them. And if you are reasonably trustworthy, they do, depending on the situation. This one isn't about trust, because there's no way to know if something goes wrong.
Plan your presentation for after dinner. Do the dishes and clear the table and ask for 15 minutes of their time. Let us know how it went.
Oh and if you lose... don't look mad, just sad. Your reaction might be needed for another try.

As a mom to two teens, both older than you, I have to say that I like Joys plan. That plan would work on me.

One thing I can add, if I say no to something and my kids continue to ask, continue to nag, I will never reconsider. In fact, it will make my no a permanent no. So don't nag at them. Present your case, and if they say no, say, "I accept your answer, but would like the opportunity to present my case to you again in the near future", then let it go until the near future.