>type data
Line 1: Header
Line 2: Keep me!
Line 3: Join me to the previous line.
Line 4: Keep me!
Line 5: Join me to the previous line.
Line 6: Keep me!
Line 7: Join me to the previous line.
Line 8: Keep me!
Line 9: Join me to the previous line.

>perl -pe"BEGIN{<>} chomp if $. % 2 == 0" data
Line 2: Keep me!Line 3: Join me to the previous line.
Line 4: Keep me!Line 5: Join me to the previous line.
Line 6: Keep me!Line 7: Join me to the previous line.
Line 8: Keep me!Line 9: Join me to the previous line.