wc -c < filename (short for word count, -c prints the byte count) is a portable, POSIX solution. Only the output format might not be uniform across platforms as some spaces may be prepended (which is the case for Solaris).
Do not omit the input redirection. When the file is passed as an argument, the file name is printed after the byte count.
I was worried it wouldn’t work for binary files, but it works OK on both Linux and Solaris. You can try it with wc -c < /usr/bin/wc. Moreover, POSIX utilities are guaranteed to handle binary files, unless specified otherwise explicitly.