The following has been in the site rules/guidelines for a long time, but hasn't been actively enforced lately:
"Signatures should follow all the guidelines and rules that apply to posts. In addition, any reference to a user on this site should be removed immediately if that user asks you to."
With the move toward an "adult" vs. "family/work-friendly" split in discussion forums (SE and GD), I wanted to re-emphasize this rule regarding signatures. Your signature appears attached to every post you make, and will therefore be held to a higher standard. As a general rule of thumb, if you can't post it in GD, don't put it in your signature.
The same applies to avatars - additionally, it has always been the policy of this site to remove avatars which are particularly attention drawing (specifically rapidly-flashing animated avatars).
If you see a problem with a user's sig or avatar, please report it to me by PM.