The sort of tenets Amazon uses are generally vague enough to abused by management constantly. I wouldn't say they are "popular", rather
forced down your throat. They're constantly mocked and poked fun at by ICs.
A good tenet is unambiguous in application and interpretation. There's no way to misuse a good tenet. Some of Amazon's are incredibly easy to abuse: frugality, disagree and commit, be right a lot. Here are some strong ones that may or may not be useful to your company:
If a decision is easy to reverse, don't spend to much time figuring out of it's the right decision.
Prioritize paying for something over building something assuming the annualized cost of an engineer is ~$X (e.g. $1MM).
Document and test internal systems as if you were selling them to a customer.
Simple, repetitive and dumb over complex, convenient and smart.
Plan to throw the first iteration away.
Be honest, and be honest to customers.
Always assume disaster can and will strike at the worst possible time. Better safe than sorry.
Prioritize people over processes. This means don't follow some dumb process if it makes everyone upset. Change the process.
Admit when you were wrong.