Do you have to pay for an accidentally broken vase?

If you broke the vase in a store, it depends on store policy. Some have very clearly posted signs saying "You break it, you buy it," in which case yes, you do.

If they don't force you to pay for the vase it is probably good etiquette to pay for it or part of it anyway, because you did cost them the sale of that item.

If this is a vase belonging to someone you know and you accidentally broke it, see if they ask for payment. If they do, even if you don't agree that you should have to pay for it, it's probably a good idea, to keep the peace. If not, know WHY not. Some trinkets like that have a lot of sentimental value and some are easily replaceable. If it is the latter, buying them a new one is a nice gesture. If it's the former, a sincere apology, even an apology card, and possibly a new vase or other gift, is best.