The best replacement for gzip is bzip2.

The best alternatives to gzip are rated as following:
★★★★★  bzip2
★★★★  deflate
★★★★  zip
★★★★  bzip
★★★★  tar
★★★  compress
★★★  zlib
★★★  winrar
★★  gunzip
★★  7zip
★  xz
★  pkzip
★  deflate apache
★  tar.gz
★  rar
★  snappy
★  minify
★  pigz
  deflate compression
  zcat
  gz
  7z
  mod deflate
  lzw
  zip compression
  lzo
  bz2
  compress unix
  x gzip

Your alternative for gzip is not listed? Suggest!
Speaking about gzip, one probably shouldn't forget about tar.

Other search terms related to gzip and their ratings are:
★★★★★ tar
★ tar command
multiple files
zlib
You have in mind a companion for gzip and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of gzip in all years. Click on graph for more.
gzip
bzip2
deflate