The best replacement for hashing is encryption.

The best alternatives to hashing are rated as following:
★★★★★  encryption
★★★  indexing
★★  binary search tree
★★  encoding
★★  encryption passwords
★  encrypting
★  skip lists
  symmetric encryption
  open hashing

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Speaking about hashing, one probably shouldn't forget about chaining.

Other search terms related to hashing and their ratings are:

★★★★★ chaining
★★ open addressing
collision resolution
You have in mind a companion for hashing and it is not yet here? Propose!

Google Trends

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