When reviewing suggested edits, should I approve them when only the signature is removed. Even though signatures are unwanted, I am inclined to reject these kinds of edits, because they are too minor.
Removing a signature can be a trivial edit. Users who post with signatures probably are unfamiliar with the system, and are likely to have made other errors in their post. These other improvements should be made simultaneously with the signature edit.
As others have pointed out, serial signature removal by suggestion-only editors is discouraged because it clogs the edit queue with trivial, but more importantly, incomplete edits. We want to discourage this behavior.
If the edit completely fixes the post
If the signature is the only part of the post which needs an edit, then approve it! The post is now completely fixed, there's nothing else to do. Don't reject the edit because it's trivial, the change needed to be made and the post is now perfect, like a majestic, dew-flecked unicorn. (<- Link is safe to click, it's an MSO post. Besides, you know you can't resist.)
If the edit is incomplete, you are willing to improve it, and there's no pattern of these incomplete edits
If you see something that needs to be improved in a suggested edit, use the "Improve" button to... improve it. That's what the button is there for. From the FAQ:
Note that this implicitly accepts the proposed edit. If you feel that the edit should be rejected (the improvements are easy and obvious), but you want to fix the problems (and remove the sig), then lend your support to this "Reject and improve" button feature request.
The number of users willing to spend time reviewing suggested edits is limited. The number of users who can suggest edits is huge. These users need to respect that the reviewers are limited, and avoid wasting their time.
Signatures are frequently repetitive edits. One user, who used a signature a long time ago, may have dozens of posts with the same signature problem. Adding a suggested edit to all of these posts not only fills the edit queue, it also consumes the time of the suggester and approver (2 approvers on Stack Overflow) and clogs the front page with useless edits, pushing important stuff away. We don't want this, old signatures aren't more important than what's already on the front page. This is something which should be done by people with edit privileges, a small number of posts at a time.
Reject these edits to train users to make more complete edits.
YES, If the only thing that needed to be fixed was the signature then
NO, If more needed to be fixed, in which case you can either
If the suggested edit just removes the signature, but there is something else that should be corrected, such as formatting, punctuation, or spelling, then the edit is possibly a minor edit.