sed '/^$/d' /path/to/input/file.txt > output.txt
grep -v '^$' /path/to/input/file.txt > output.txt

#!/bin/bash
files="/path/to/input/files/*.txt"
for i in $files
do
  sed '/^$/d' $i > $i.out
  mv  $i.out $i
done

#!/bin/bash
files="/path/to/input/files/*.txt"
for i in $files
do
  sed '/^ *$/d' $i > $i.out
  mv $i.out $i
done