Canning

Yes, I have to agree with everyone else.
Canned/jarred goods generally need refrigeration once opened.
But that's why mason jars are relatively small, once you open a can of tomatoes you make sauce, once you open a can of fruit you bake a pie, you get the idea.
The only things with the kind of shelf life you are looking for are dried foods: spices, pasta, rice, beans, oats, jerky, nuts/nut butters, honey, etc, and of course oil and vinegar.

All the canning does is prevent spoilage during storage... once opened, they can quickly become contaminated by bacteria.

I'm not sure if there is anything that fits your requirements that can be canned at home without additional commercial preservatives....

Sorry, but even jam has to be refrigerated once it's opened. Not surevwhat wouldn't need to be ... Perhaps Ball's website can offer you some help.

http://www.freshpreserving.com/home.aspx

Best wishes.

I can't think of anything that wouldn't need refrigeration...

Maybe pickled eggs or sausages? I have seen them at gas stations on the counter, so I'm assuming they are ok not to refrigerate once opened... but blegh. lol.

Jams don't need to be refrigerated if the sugar content is high enough. If you are skimping on the sugar they will need refrigeration
Certain pickled vegetables can go a few days without refrigeration as well. If you are storing them out of the fridge once opened they tend to get soft and change in color - going too long (weeks) they will grow mold. But yeah, a few days is fine.

If you are not having a fridge, just can in smaller jars so you can use up whatever it is in a day or two.
Even though modern Americans think that pretty much everything belongs in a fridge (and to be fair refrigeration cuts down on foodborne illness) most of they world (gasp) does not have access to a fridge and people deal with it just fine. Even things like eggs, butter, cheese and some processed meats can go without a fridge if they are kept in a relatively cool place.
Good luck.