Update: Sort of ironically, this question has been left unedited for a while, even when there seemed to be some consensus in the answers below of the kinds of edits that are acceptable and those that are not. So I'll do my best to update it with what seems to have been the consensus in the end. As usual feel free to edit and open new answers to discuss any new issues.
Following the discussion on deciding when is it acceptable to edit others' answer?, this question is an attempt to summarize the consensus reached by the community.
Add links and references. This includes fixing links pointing to broken/obsolete content.
Fixing tags. To use more clear or precise tags, or to remove the use of discouraged tags.
To improve formatting. For example badly formatted code, URLs pasted in the text without a description, or in general incorrect usage of markdown formatting.
Adding pictures. This is particularly useful when a question/answer can be made clearer by compiling the example code provided by the original author, and then adding a picture that shows how the output looks.
Fix typos in the code. Repair minor typos in the code of an otherwise well written question or answer.
To change the original meaning. It is unacceptable to edit someone else's question/answer and, in doing so, change its meaning or intention (e.g., what is discussed in the Meta Stack Overflow discussion about abusive editors).
As a corollary, one shouldn't edit the question if one is unable to understand the meaning of the original question.
Adding new information. Particularly for an answer, additional information that could improve it should be added as a comment (which can be upvoted!).
If there is a significant amount of information that you wish to add, consider adding a new answer instead and credit any previous information you take from other existing answers.
Fixing typos or grammar errors. Editing a question/answer for such small issues has the undesired effect of bringing the question back to the homepage, which can become a nuisance for frequent users of the site.
There are two obvious exceptions for fixing these types of errors: 1. you are editing for one of the acceptable reasons anyway; 2. the question is near to the top of the active questions anyway.
faqtag is also probably not desirable. Any ideas of what could we do?