First, keep in mind that when SE was younger, there was a lot of room for new badges. As the system has matured, there simply isn't as much need for new badges any more. So while it's true that a lot of those old badge requests were created by users, the fact now is that squeezing in a new badge is tough. You better be convincing.
What makes a good badge proposal?
A good badge proposal:
- Encourages positive behavior.
- Helps sites thrive and promotes an effective Q&A model.
- Does not conflict with existing site goals, contradict existing mechanics, create more work for moderators, etc.
- Often includes a thoughtful analysis of the effects of the badge (both good and bad).
I've observed that many well-received requests seem to encourage the posting of great quality questions and answers, and that many poorly-received requests seem to encourage dishonest voting and increased noise.
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 others). Sometimes, you might even want to consider proposing a hat instead.
When, and why, should new badges be proposed?
There isn't really a good answer to this question; there is no hard and fast criteria. As MSE is free, open, and exists to allow users to propose and discuss site changes, personally I believe that a new badge should be proposed whenever you think of one, noting that when a badge should be proposed is different than when a badge may be needed. Make all the proposals you want, whenever you want. That's what metas are for.
As for when a badge may be needed, in my opinion, some examples among others:
When a certain positive behavior is theoretically desired, but realistically not happening (or not happening enough). Deputy and Marshall are sort of good examples of this (I'm open to a better example): We want helpful flags, but without encouraging them with a reward, we may not get enough of them.
When an observed behavior leads to increased question and answer quality, and so reinforcing that behavior improves the sites. The Undeterred and Red Baron proposals in the examples below are good examples.
When there is a legitimate, big picture, systemic problem caused by negative behavior, and no site mechanics have really been able to turn it around.
I'm sure there are many other reasons.
When is a new badge not the solution?
There are a lot of answers to this as well. In general if you are unsure if a new badge is the solution, the easiest way to find out is to propose it. The community will most certainly let you know!
One red flag, I think, is that if you did something that you are feeling particularly peachy about (such as posting a funny comment and receiving a lot of comment votes), and you decide that you deserve a reward for it, this is often a recipe for a poorly-received proposal. Be sure to think about what behaviors your proposed badge encourages and what the bigger picture effects are.
Another red flag is proposals born from irritation: If somebody, say, downvotes one of your posts without leaving an explanation, and you are upset about it, a proposal for a badge to make that not happen usually doesn't go well. Again, be sure to consider the bigger picture.
Here's a few examples that I think illustrate the above.
Poorly-received or status-declined:
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?
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 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?
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.