The best replacement for sha1 is md5.

The best alternatives to sha1 are rated as following:
★★★★★  md5
★★★★  sha256
★★★★  sha2
★★★  sha512
★★  bcrypt
★  md5 speed
★  sha
★  md5 faster
★  md5 php
★  md5 more secure
★  md5 encryption
★  md5 checksum
★  md5 hash
★  md5 vpn
★  crc32
  hmac
  sha 512
  md5 better
  3des
  tripledes
  md5 performance

Your alternative for sha1 is not listed? Suggest!
Speaking about sha1, one probably shouldn't forget about dsa.

Other search terms related to sha1 and their ratings are:
★★★★★ dsa
★★★★ rsa
★★ rsa encryption
You have in mind a companion for sha1 and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of sha1 in all years. Click on graph for more.
sha1
md5
sha256