I don't have a specific order so lets start

• the [bloomfilter algorithm . It's such an interesting idea to visualize, it's like a shape and everything that is inside that shape can pass through but it also includes false positives. so it's a real nice pre-filter system/algo.
• robinhood hashing since a normal hashmap already has O(1) which means constant time the robinhood hashing optimizes the hashmap to be even more efficient on reads. It's such a simple and beautiful idea take it from the rich give it to the poor
• huffman coding we're becoming quite ignorant on fault tolerant transmissions and regularly dismissing the complexity of impendance or jitter or other forms of loss of information and his algo is not the best but it was one of the first fault tolerant predictive algorithms and it's still beautiful :) and one of many reasons we still can communicate with our space probes
• GZIP-Algorithm if you have to ask why a low cost average compression algorithm is appreciated in the web-development you should read up on it
• the Thompson's construction because I just like formal language analysis and syntheses
• Hilbert's paradox of the Grand Hotel because using countable infinity with prime numbers in Master-Master-Replications is just awesome :D .....
• Dijkstra's path algo this is one of the algorithms we probably use in so many aspects of our life :D

and there are so many more :)

Burrows Wheeler Transformation - allows you to transform a string into something that's much easier to compress.

I like the TimSort algorithm very much. It was mentioned last year but found it recently on Twitter again.

Timsort is a hybrid stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data.

Next on my list is density. A super fast compression algorithm with very promising results.

It is focused on high-speed compression, at the best ratio possible. Streaming is fully supported. DENSITY features a buffer and a stream API to enable quick integration in any project.

http://hashids.org/

Hashids is a small open-source library that generates short, unique, non-sequential ids from numbers. It converts numbers like 347 into strings like “yr8”, or array of numbers like [27, 986] into “3kTMd”. You can also decode those ids back. This is useful in bundling several parameters into one or simply using them as short UIDs.

Bonus: Compressing UserTiming

github.com/nicjansma/usertiming-compression.js