I'd like Jump rules to make jumping realistic at low levels, and then make it useful at high levels. A 1st level character should easily be able to jump 5 ft., and have the possibility of clearing a 15 ft. gap with a heroic effort. A 10th level character should be able to easily clear that 15 ft. gap, and be able to pull off Matrix jumps. I mean, at the same level we have wizards teleporting. A bit of heroic jumping won't break anything.
How about:
All characters can jump a distance equal to one-tenth their base speed as a standing jump, or twice that if they have a 20 ft. start. So typical human, when not straining himself, can jump 3 feet from a standing position, and 6 feet with a running jump.
Characters who need to jump farther make a Jump check, then consult the following table to see if they can clear the necessary distance. For running jumps, double the distance at any given DC.
Let's remove the existing bonus/penalty to Jump checks based on base speed.
Additional Feet . . . Jump DC
. . . . 1 . . . . . . . . . . 10
. . . . 2 . . . . . . . . . . 14
. . . . 3 . . . . . . . . . . 17
. . . . 4 . . . . . . . . . . 20
. . . . 5 . . . . . . . . . . 22
. . . . 6 . . . . . . . . . . 24
. . . . 7 . . . . . . . . . . 26
. . . . 8 . . . . . . . . . . 28
. . . . 9 . . . . . . . . . . 29
. . . .10 . . . . . . . . . . 30
. . . .11 . . . . . . . . . . 31
. . . .12 . . . . . . . . . . 32
. . . .13 . . . . . . . . . . 33
. . . .14 . . . . . . . . . . 34
. . . .15 . . . . . . . . . . 35
. . . .17 . . . . . . . . . . 36
. . . .20 . . . . . . . . . . 37
. . . .23 . . . . . . . . . . 38
. . . .26 . . . . . . . . . . 39
. . . .30 . . . . . . . . . . 40
A character min-maxed for jumping can get pretty impressive jump checks, even in the core rules.
Core Rules
Half-Orc Barbarian 1/Rogue 1, 5 ranks Jump, 5 ranks Tumble, Skill Focus (Jump), Str 20. While raging he has a +17 bonus to Jump checks (+21 in the core rules because of his fast movement), so he can Take 10 and clear a 31-ft. gap on a running jump, or making a 15-ft. standing long jump.
Half-Orc Barbarian 11/Rogue 1, 15 ranks Jump, 5 ranks Tumble, Skill Focus (Jump), Acrobatic, Str 27 with belt of strength +4 (33 when raging), ring of jumping +10. While raging he has a +43 to Jump check (+47 in the core rules because of his fast movement). He can Take 10 and make a 28 ft. standing long jump. With a running jump he can clear 57 ft., or get an 14 ft. vertical Jump.
Half-Orc Monk 12, 15 ranks Jump, 5 ranks Tumble, Skill Focus and Acrobatic, Str 27 with belt, ring of jumping has +40 to Jump (+56 because of fast movement).
A half-Orc Monk 15/Druid 5 could wildshape into a Cheetah and, as part of a charge, get a speed of 550 ft, which would grant a +208 from speed. Add that to other jump bonuses at 20th level (23 ranks, +2 synergy, +5 from feats, likely +10 item, +10 Strength), and you've got a +258 bonus to Jump checks.