The best replacement for rar is zip.

The best alternatives to rar are rated as following:
★★★★★  zip
★★★★★  7z
★★  win zip
★★  tar
★★  winzip
★★  rar5
★  zip file
★  zip better
★  rar 5
★  zip compression
★  7zip
★  zip smaller
★  gzip
★  zip better compression
★  zip files
★  exe
★  xz
★  zip which is better
★  bzip2
  par
  .tar
  lzma
  zip difference
  7 zip
  .zip

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Speaking about rar, one probably shouldn't forget about 7zip.

Other search terms related to rar and their ratings are:
★★★★★ 7zip
★★★★★ winzip
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Google Trends

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rar
zip
7z