The -e conditional operator tests whether a file exists (including all file types: directories, etc.).

if [[ -e $filename ]]; then
  echo "$filename exists"
fi

There are tests for specific file types as well.

if [[ -f $filename ]]; then
  echo "$filename is a regular file"
elif [[ -d $filename ]]; then
  echo "$filename is a directory"
elif [[ -p $filename ]]; then
  echo "$filename is a named pipe"
elif [[ -S $filename ]]; then
  echo "$filename is a named socket"
elif [[ -b $filename ]]; then
  echo "$filename is a block device"
elif [[ -c $filename ]]; then
  echo "$filename is a character device"
fi
if [[ -L $filename ]]; then
  echo "$filename is a symbolic link (to any file type)"
fi

For a symbolic link, apart from -L, these tests apply to the target, and return false for a broken link.

if [[ -L $filename || -e $filename ]]; then
  echo "$filename exists (but may be a broken symbolic link)"
fi

if [[ -L $filename && ! -e $filename ]]; then
  echo "$filename is a broken symbolic link"
fi