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In endgame, you typically have a hand in tenpai that is waiting for 1 more tile to be complete. Usually, it is better if you are able to wait for multiple tiles so your chance to finish are increased. From the rules, some typical wait patterns are derived. For instance, if you got 3 sets and a pair and an incomplete 23, you're waiting for either 1 or 4 to complete a chii (street).

Experienced players know that certain patterns lead to especially high chances to finish. What are the most common patterns to know and strive for?

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I found a basic answer on my question over here:

Try to go out waiting for multiple tiles (not just one). Imagine that you have three complete sets and two pairs. Imagine that one pair is 2 Bams, and you draw a 3 Bam from the wall -- which tile do you discard now? In this situation, many experienced players will discard a 2 Bam, keeping 2-3. A two-way incomplete chow call is better than a two-pair call.

Learn to shape the hand into calling patterns that give you multiple chances to win, such as the following:

Tiles in hand     Call for 

2223              134 
2224              34 
2223344           2345 
2223334           2345 
2223456           14736 
22234 RR          25 R 
23456             147** 
34567             258** 
45678             369**

Highly skilled players of un-American mah-jongg (since American style alone does not use "chows") know these patterns by heart. More complex call shapes are mostly extensions of these. Although the American game does not use chows, the strategy of having a multiple-tile call still applies to that game as well.

Of special interest is the complexity of the pure hand. If you're working on a pure hand, it can often be difficult to tell what all the tiles are that can complete the hand. For instance: 1-2-3-4-5-5-5-6-6-6-7-8-9 (5 chances); 1-2-3-4-5-5-5-5-6-6--7-8-9 (5 chances); 2-3-4-4-4-5-5-5-6-6-6-7-8 (7 chances); and of course 1-1-1-2-3-4-5-6-7-8-9-9-9 (9 chances).

Edit: Additional links with a lot more waits

Especially the latter is, from my beginner eyes, insanely exhaustive.

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Update January 2023:

There is a Mahjong Waits Infographic which shows common patterns: Common and Useful Mahjong Wait Patterns

Links: PNG | PDF | Author's post (Reddit)

Original answer

As an additional resource, I created a tool for finding the waits needed to complete a hand: https://mahjong-trainer.netlify.app

It generates random tenpai hands, so you indicate the waits and the site will tell you the correct answer. And after some tries you'll start to spot some wait patterns.

Screenshot:

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