I know we need 1500 points to be able to create tags on Stack Overflow.
Now I wonder about the rules around removing or editing tags.
Would it need consensus of a certain number of people to approve the operation to be effective?
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There is a purge script that runs daily to delete all tags without any questions. We have a process called burnination where a community consensus can be reached on tags that should not exist, for multiple reasons.
After burnination, a tag can be removed by a mass editing effort where all instances of the tag are removed from all questions. Note that burnination is mostly used on tags with > 50 questions.
If you accidentally create a tag, you can remove it yourself by making sure you remove it from the post where you created it. If you think there is a similar-enough tag, you can assign it as a synonym of another tag, or ask on the site's Meta if you don't have enough reputation.
Basically: there's no "proper" function to delete tags, but you can have it done by making sure the tag has no questions.
Anyone can edit or suggest an edit that removes a tag from a question.
Whether your edit needs to be approved will depend on your reputation level. Users achieve the Edit questions and answers privilege on this site at 2,000.
I recommend waiting until you reach that privilege before attempting to make too many tag changes because tagging schemes have often taken around a decade to evolve to their current level of effectiveness.
Tag addition or deletion is simply an edit, or suggested edit. See: "How do suggested edits work?
If a tag ought to be removed because it's inappropriate, or to make way for a much more useful one, you can do so; but you might be risking a rejected edit.
To add a new tag read what you wrote and try to define the subject in one word, type part of the word into the tagline and see what the search suggests. Hyphenated words are also used, so try to check the sub-topic. For example, don't just type "windows", say which: windows-7 × 13, windows-8 × 6, windows-phone × 12, etc.
If you create a new tag it's polite and helpful to write a decent excerpt, and even nicer to complete the tag wiki.
The advice offered on the tags page is:
"A tag is a keyword or label that categorizes your question with other, similar questions. Using the right tags makes it easier for others to find and answer your question.".
What's the point in ultra focused tags like [resultset] ? Can we remove them from questions? - Too specialized or way too general is not useful, usually.
Usage and removal of tags - Seven year old advice, with few upvotes and views, but a close duplicate.
Should we prefer tags with hyphens? - Use unambiguous tags.
For new tags there's some great advice here: How can I edit tag wiki entries?