Is there a function to return the length of a string?

The fastest way, not requiring external programs (but usable only with BASH and KornShell): 

${#varname}

or for Bourne shells: 

expr "$varname" : '.*'

(expr prints the number of characters matching the pattern .*, which is the length of the string.)

Another one: 

expr length "$varname"

(This is for a BSD/GNU version of expr. Do not use this, because it is not POSIX).