So non-dice systems.
For me the greatest non-dice random number generator of all time has to be the basic pack of playing cards. These are incredibly flexible from an RPG perspective. If you ditch the kings for example you have in your hand fore distinct d12s.
If you use the just the number cards then you have 4d10 but there is so much more you can do with the deck. You can assign meaning the the suits with the red being relating to magic, Diamonds to Essence and Hearts to Channeling, you can make Clubs strength based and Spades Quickness or Agility.
Then of course there is the classic Deck of Many Things, a real pack of cards is the perfect prop for that magic item.
There are some games that eschew dice in favour of cards as a core mechanic. Ken Wickham has his ABS12 game, in fact he has over 50 supplements he had released now and they nearly all work using 1d12 or 2d12 or with a deck of cards without the kings.
My wild west game “Devil’s Staircase Wild West Role Playing” is the first of a series of games that uses no dice at all. You are dealt a hand of cards and you pretty much play your card and add your skill to the face value. The intention is to create that poker game feel that sits quite well the Old West setting. The deck of cards is so central to the game engine that the system’s name is a reference to the cards. The devil’s staircase is a slang name for a fanned deck of cards and an allusion to playing cards being a route to vice and degradation.
In the Devil’s Staircase system the Joker plays an active role and is the games equivalent to open ended roll on the attack or the 66 on our critical tables.
The d100 may be the most granular dice for regular play but the deck of cards with 13 faces, two colours and four suits plus two jokers packs a lot of options into a very common household object.
And finally of course if your character gets killed at the start of the big fight you can still build a house out of the cards or play solitaire, that is easier than trying to play Yahtzee with d10s.