No, under no circumstances may your boss (or anyone else, for that matter) forge your signature. Doing so may constitute a criminal offence and can be tantamount to fraud. This having been said, your boss, or anyone else, may sign a letter on your behalf, but only if you have given him/her clear authorisation to do so. The difference between this and forging is that there is no attempt made to imitate your signature or handwriting. Rather, the person signing will simply write your name without any regard as to the style you would use to write it.
In some cases, your boss or others at your workplace may sign a letter as "John Smith for Jane Doe." This way it is clear to the reader that the person signing is representing someone else, but that their is no attempt to falsely claim someone's identity.
You should always think long and hard before allowing someone to sign letters and other documents on your behalf. In many cases, the best idea is to give someone you trust a power of attorney.
In some cases, your boss or others at your workplace may sign a letter as "John Smith for Jane Doe." This way it is clear to the reader that the person signing is representing someone else, but that their is no attempt to falsely claim someone's identity.
You should always think long and hard before allowing someone to sign letters and other documents on your behalf. In many cases, the best idea is to give someone you trust a power of attorney.