In many Western countries (at least before current events), the handshake dominates as a physical ritual people perform when they meet each other. Are there countries with an alternative physical ritual that people perform when meeting each other?
In France, kissing is quite common, esp. between two different genders. In some Asian countries, bowing is also quite common. There exist many other habits, see https://en.wikipedia.org/wiki/Greeting, such as:
In Japan, you bow. Handshaking is rare; bowing is many times a day.
Interestingly a lot of the stuff the world is doing now because of COVID was commonplace in Japan long before. In Japan, even before COVID, you wouldn't go out of your way to make physical contact with most other people - generally no hugging or handshaking, though exceptions existed. You bowed instead.
(As was referred to in the comments, sometimes physical contact was still pretty unavoidable, due to crowding, particularly when using public transportation.)
They were also already wearing masks part of the time, being extra careful to sanitize things with alcohol, that kind of thing.
In the Arabic world, for example Egypt, you can place your right hand on your heart and bow your head slightly.
In Arabic you can also say "Tasharafna" (it's nice to meet you).
The "hand on the heart" gesture conveys well meaning, even if the other person doesn't know this gesture from before.
It's also very practical in times of Corona, and much more polite than the "corona elbow" or "corona foot tap" gestures.
There is the Narmaskar or Namaste greeting in India: https://en.wikipedia.org/wiki/Namaste#:~:text=Namaste%20or%20namaskar%20is%20used,his%20or%20her%20generous%20kindness.
In the answer by @Franck Dernoncourt, the elbow bump has been mentioned.
It's very common, between friends, where I live**, since Covid19
I've even seen and used the "air bump"! The people making the greeting stand apart and move their elbows as though to touch without actually making contact.
** South of England