>Are there any major ones I'm missing, or even better, any lesser known ones I should be aware of?
MinHash.
I also highly recommend this blog: https://research.neustar.biz/tag/sketching/
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MinHash works well if you need to approximate Jaccard similarity. To approximate cosine similarity, you can use Charikar's SimHash: http://d3s.mff.cuni.cz/~holub/sw/shash/.