Donít burn them. Yet. The writing may be terrible and the stories ill-conceived, but you never know what you could turn those into given a few more years.
Read them again, edit them, and publish.
Keep everything, you never know when it might come in handy. I go through my files for old ideas all the time.
Pick out the really good bits and find a new home for them in your current works! Never, ever throw anything away. All it needs is some reworking.
You have to show someone you know if you want to do something with it. If you don't, keep it hidden. I didn't think about publishing my work until I had heard that it was good enough to publish by family, friends, and complete strangers. I had meager expectations and I still do. I would do the same and not think too highly until someone else gives good feedback. I hear about too many horror stories about someone who thinks their work is great, but an expert doesn't think so.
Revisit the writing. Even for the writing that you don't think is publishable as a whole, more than likely there are some gems within to extract and use for current or future projects.
SHOW IT! Don't be silly. You could be hiding the next bestseller because of insecurities or whatever else. I hid my writings for years away from others, not knowing how it would be received. Finally I had to show someone and I haven't regretted it one bit. Good luck to you!
Just write them up. Never be afraid to put yourself out there because the greatest form of flattery is something telling you they like what you wrote.
I really believe in people. I believe we are all creative and we all have our unique story to tell. Go back and read them now and see if you think they are any good. Show them to some people you trust - not people you trust to say "oh wonderful" people you trust to tell you the truth even if it isn't what you want to hear. Set down and think about it. Decide if you have the desire and passion to move them forward. Writing is hard - making yourself write, and rewrite, and edit, and sometimes throw something away or at least set it aside until you can figure out what is wrong with it and fix it. Then you have to face the facts about publishing and find out how determined you are about that. But, by all means, give yourself a chance.
anyone who writes, needs to write. bring them out and work on them. rewrite them. work them until they are so good you have to show them to someone, and then rewrite them again. and just keep writing.
Take out you work, rewrite if needed, and take a chance on asking a friend to read. You may be pleasantly surprised by the response.
This is a very personal thing and you have to decide what is best for you. I have some poems I wrote years ago which I would never show to anyone, for example.
If you read through your old work again and still love it now, perhaps it is time to show it to someone else and get a second opinion. Good luck!
Writing, by itself, is therapeutical process. So the question is, do you really think publishing those writings, even on a small scale, would bring more advantages? If yes, then go ahead and start sharing them or even try to publish them. Who knows?
Keep them somewhere in the attic. Seriously; if you throw them away, you'll regret it some day, but if they're too close, you might be tempted to try and re-work them into something you might want to show someone. And that would, probably, be a very bad idea. Usually, the first few hundred thousand words anyone writes are best forgotten. And yes, that's around a novel or two that you need to throw away before you can expect to have something decent on your hands.
Step one: Suck it up and show someone. That's always the hardest thing to do. After that, start editing and see if you can make something of the piece. Take a writing class or workshop. But you know what? If that old stuff isn't working for you, move forward. Start writing something that reflects where you are at right now!