I've also observed that Winter Bash seems to be a great test bed and inspiration for new badge proposals (see, for example, the Red Baron and Weed Eater proposals at the end of this post, among othersamong others). Sometimes, you might even want to consider proposing a hat instead.
Badge to promote upvotes?Badge to promote upvotes?
While "upvote" has a positive connotation and so at a glance this suggestion may seem "positive", it damages the site model by encouraging upvotes for the purpose of gaining a badge, rather than encouraging honest voting based on the merit of a post.
Proposal to add a "Circlejerk" badgeProposal to add a "Circlejerk" badge status-declined
Granted this seems to have been posted as a joke, but it is a good example of a bad suggestion. Obviously, a group of users upvoting each other is not positive behavior.
New badge suggestion for high negative scoreNew badge suggestion for high negative score (and it's linked dupelinked dupe) status-declined
There is nothing positive about having a high negative score, and the badge potentially encourages users to make bad posts simply to gain the badge.
"Post-it" badge for totally epic comments"Post-it" badge for totally epic comments status-declined
While this seems fun, and fun is good, the fact is that sites discourage chatty comments (there's even a flag for it), and this conflicts with the site model of what a comment should be.
Undeterred badgeUndeterred badge
Encourages and rewards a positive behavior, with criteria that naturally resist gaming the system to gain it (the goal is to write a post of such good quality that it changes the asker's mind, and if a user writes great quality posts simply to gain a badge, everybody still wins).
Should we make the Red Baron hat trigger a permanent badge?Should we make the Red Baron hat trigger a permanent badge?
This proposal contains a very thoughtful analysis and makes a great case for a badge whose observed behavior (from hats) notably encouraged great posts.
Reward <3k reputation users for finding duplicatesReward <3k reputation users for finding duplicates
This is a well-written proposal for a badge that encourages a behavior that ultimately helps out a site, essentially training new users to help find duplicate questions. Even though there may be downsides, the proposal itself considers them thoughtfully.
Can we add a badge having similar criteria as Weed Eater hat?Can we add a badge having similar criteria as Weed Eater hat?
Like the Undeterred proposal above, this encourages and rewards a positive behavior, with gaming-resistant criteria. The goal is to write a good post to a not-terrible question that did not receive a lot of attention.