What are the best rules you've ever seen for leaping in D&D or in any other game?
I'm looking for an ultra-precise leaping simulator or for wishy-washy narrative leaping; I'm just looking for something fun and serviceable without being too random.

If its just based off a Strength check or skill check, how random it is depends on what core mechanic you're using; its not surprising 3E has a page of jump rules because its trying to use a D20, but rolling 3d6+modifiers would be OK, dice pool likewise is a bell curve and probably OK (e.g. Vampire = roll Str+Athletics) though it could be a bit granular since your baseline human is only rolling 2 dice. Multidie additive systems like D6 System probably give quite good results just with a Strength or Athletics check as well.

If you don't have a system where the main game mechanic gives reasonable results, my preferred option is probably to just have a fixed Jumping distance (based off Strength e.g. Str/2 depending on the scale) and then have another rule elsewhere on how a character can 'Push' their strength in emergencies with a roll of Willpower or something- which could be used for jumping, lifting, whatever.

For Blood & Iron, I have a table based on a character's Strength + Agility for running long jumps, running high jumps, standing long jumps and standing high jumps.

I can't post the table directly because It would lose the formatting, but you can download the pdf in my sig. It's at the bottom of page 110 (page 116 according to Adobe Acrobat).

1e Dungeoneer's Survival Guide has a base jump distance of 1d4+5'. That seems to work ok for 'grounded' fantasy.

The worst jump rule I know is the 3e/4e one where you roll a d20+skill check and the result equals the number of feet you jump, so 1' to 20' base, or a typical PC with a +10 mod is jumping 11'-30'. One counter-intuitive result of this is that it's a lot easier to jump over difficult terrain than walk through it.

Yeah, I'm not happy with d20 based jumping. That's a big part of why I'm asking about this.

Here's an idea!

Speed is expressed in the form of a movement die based on how heavily encumbered you are.
Unencumbered 1d12
Lightly Encumbered 1d10
Moderately Encumbered 1d8
Heavily Encumbered 1d6
Over-encumbered 1d4

Whenever you move, you can choose to roll the movement die to see how far you can go in inches/squares/paces/increments-of-five-feet or you can take the average result.
You take the average result when you are moving slowly and deliberately across the ground (I.E. walking), and you roll when you move dangerously (I.E. leaping).

I don't see jumping as that random. Try this -

Str + Dex / Standing Long / Running Long / Standing High / Running High
6 - 8       /        3 ft.       /      8 ft.       /      1 ft.         /     2 ft.
9 - 12     /        4 ft.       /     10 ft.       /      2 ft.         /     3 ft.
13 - 17   /        5 ft.       /      12 ft.      /      2 ft.         /     4 ft.
18 - 24   /        6 ft.       /      14 ft.      /      3 ft.         /     5 ft.
25 - 29   /        8 ft.       /      18 ft.      /      4 ft.         /     6 ft.
30 - 33   /        10 ft.     /       22 ft.     /      4 ft.         /     7 ft.
34 - 36   /        12 ft.     /       28 ft.     /      5 ft.         /     8 ft.

Maybe for each level of encumbrance, you move "down" a level.

The averages and maximums are calibrated to human averages and olympic records (old ones, but nonetheless)