The best replacement for hydrogen bonds is covalent bonds.

The best alternatives to hydrogen bonds are rated as following:
★★★★★  covalent bonds
★★★  ionic bonds
★  van der waals bonds
★  dipole dipole
★  dipole-dipole
  covalent
  van der waals attractions

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Speaking about hydrogen bonds, one probably shouldn't forget about dna.

Other search terms related to hydrogen bonds and their ratings are:
★★★★★ dna
★★★ water molecules
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hydrogen bonds
covalent bonds
ionic bonds