Here's a game design breakdown for jumping in Valve's seminal Counter-Strike.
(2 fixed heights (no phys control and timing/speed phys control (crouchjump)), length based on speed (some phys control), mouse direction air control (no momentum air control)(some phys control), no cooldown.
But due to quake engine physics behavior we have the possibility of bunnyhopping (timing, phys control of mouse and keyboard in alternating rhythm) which gives movement around the map at greater speed than usual (but can't really aim at the same time).
Falling damage means that jumping from great heights is not usually effective competitively, but short drop-downs are often used to surprise.
Does not usually provide a combat advantage in the open, since it reduces midair accuracy of all guns except shotguns (here it can be used to jump-shoot over low walls or to present a more difficult to hit target, and give easier angle for headshots).
Can be used to obtain vision of enemy by jump-peeking, often in combination with sniper rifle or to counter a sniper who's scoping a spot.
Level design and jumping: navigating the environment without jumping at all is possible in most levels. Jumping, however, often provides a speed advantage in getting to certain positions (box jump in t spawn to b rush on de_dust2), or is required for safe transitions (jumping into pit at long A in de_dust2), or in combination with boosting (jumping on another players head) can be used to get to various spots that would otherwise be unreachable (providing speed, safety boosts) (examples de_dust2 ct spawn-box-short a boost, inferno apt window boost (t usually)). Many areas with crates/boxes etc. require jumping in order to navigate (boxes outside de_dust2 b site)
There are also player made jump challenge or trick maps (mostly based on timing and using slight aircontrol in very difficult ways or bunnyhopping).
Low gravity and airspeed/control on scoutzknivez make air navigation and jumping/aircontrol central elements of gameplay on that map. Low gravity on other maps also makes jumping more important, but this map is the main one where it really drives and improves gameplay (in combination with scout, vertical arrangement of map, etc.)