I find the jump rules somewhat conservative and complicated to... boot. Sorry bad pun. Love to see something more clean cut and dare I say, dramatic. let the player jump 20 feet or 2 stories straight up, etc. The vertical height that athletes in basketball and football can achieve is amazing. Love to see the boot make the wearer better then that :-).

You make an interesting point about the vertical jump, but I believe you're not addressing some factors.  Basketball, football, volleyball, high jump, and really any other sport that holds jumping as a tenant of the sport have one thing in common - most of their gear (football being the exception) is of negligible weight.  Adventurers in the D&D world are wearing/carrying in excess of 50lbs while some adventurers carry over 100lbs without suffering encumbrance (even higher, still, for STR-based PCs).

If you had a basketball player piggy-back someone of 100lbs and try to dunk, very few would be able to do it.  These boots, to think of it in a way that's not conducive to the rules and rather is just for conceptual application, are removing the weight of the gear and items people are carrying and, therefore, allowing them to jump as if they were not carrying/wielding any of those items.

http://fexlabs.com/5ejump/

Heres a jump calculator to make it easy!

I just let the player wearing these use all her movement as jumping.  She can jump 30 feet straight up if she wants.  It's not strictly how its supposed to work but its much faster and more dramatic.

Quote from Toadsen >>

http://fexlabs.com/5ejump/

Heres a jump calculator to make it easy!

 You are doing the lords work !

One thing RAW doesn't address is how these affect falling damage. 

Normally characters take 1d6 per 10' fallen. With these boots a character with (e.g.) a 19 ST a dwarf could jump 20' into the air... so what happens when he lands? Does he take 2d6 falling damage? And if the answer is no... then what happens if he genuinely falls 20' (instead of it being at the end of a jump)? And if the answer is still no, then how far can a character fall without taking damage while wearing these boots?

Also how do the boots prevent one from jumping the full distance? I mean for a horizontal jump with a 19 ST and a running start a human could jump 60'.

So lets say you've already moved 30' and now you take the move action and jump... does it mean that suddenly the boots don't have enough power to jump 60'? Or does it mean your character plummets to the ground magically after 30'? Or does one just have to make up some nonsense like – "because you've already moved 30' you can't find the stamina to jump to the full extent the boots are capable of"?

There are three ways to look at this that I can come up with: 1) We have to think about time, this is happening in 6 seconds, so unless you use the dash action, once you run 30 feet, you don't have enough time to jump on that turn.

2) Let's say you move 10 feet to get a running jump start and you go for a high jump, well once you reach 20 feet in the air, you will "freeze" there from a game time perspective and won't go the other 10 feet until your turn starts up again and then you will fall 30.

3) Outside of turn-based combat, this will not apply because the whole "30ft" of movement, most people start with also only applies in turn-based combat and will become a continuous and constant 30 feet (or 60 if dashing) every 6 seconds without an end until turn-based combat starts up again. So if you are not doing things by 6 second turns than you will definitely be able to dash 60 feet fowards and than dash again 60 feet up. Enjoy!

What if your character is carrying less than 5 lbs of equipment such as a monk with the Outlander background 

The caption reads Basic Rules, pg. 156 but in my PDF it's pg. 168. FYI.

Actually it makes sense, not because you "can't" move, see it as "the time of your turn ran out". 

Quote from geoidesic >>

One thing RAW doesn't address is how these affect falling damage. 

Normally characters take 1d6 per 10' fallen. With these boots a character with (e.g.) a 19 ST a dwarf could jump 20' into the air... so what happens when he lands? Does he take 2d6 falling damage? And if the answer is no... then what happens if he genuinely falls 20' (instead of it being at the end of a jump)? And if the answer is still no, then how far can a character fall without taking damage while wearing these boots?

 Yeah, they'd still take the falling damage because there's nothing that says you don't in the boots' description, however there are ways to avoid fall damage, such as a caster casting feather fall on you (or yourself casting feather fall if you can) or a 4th level monk's slow fall reaction
And if you want to be technical RAW does address fall damage. Because specific beats general, if these had any specific way they affected fall damage, they would say so, but because they don't affect it, they don't specify anything and you go back into the general rule.

I’m trying to pick random magic items to describe as daelkyr creations so I’m better at that if I ever get to run an Eberron campaign.

“Kyrzin, the daelkyr Prince of Slime, awards these chunks of sludge to those who tend to its lovely creations; Slimes, gibbering mouthers, and the like. They allow for you to move perfectly freely, sliding over any obstacle you encounter like a slime could”

So then is it feasible to say that a basketball player wearing these shoes could make a "Full Court" Dunk?

I'm wondering how these interact with the grappling mechanics. When you have someone grappled your speed is halved, but these set your walking speed to thirty. Anyone have thoughts on this?

Quote from LochTessMonster >>

I'm wondering how these interact with the grappling mechanics. When you have someone grappled your speed is halved, but these set your walking speed to thirty. Anyone have thoughts on this?

I'd rule that if you're wearing these and you're grappling, your speed is 15.  Too OP for an uncommon item to make it so you can NEVER lose speed.  These boots don't say anything about grappling, or anything else that reduces speed.  Since specific beats general, I think it's fair to say that the boots adjust the base walking speed, but other conditions can be applied on top of that.  For example, these say nothing about difficult terrain, so I would rule that affects your speed even with these boots on as well.

This + the Jump spell = even a skinny wizard can long jump 72 feet :D

Hmm. But how much could/can you carry while wearing the boots? we have a player that thinks he can basically carry an unlimited number of items as long as he has the boots

Well, what non-speed related consequences are there to encumberance?

I am trying to add the Boots of Striding and Springing to the PC, together with Plate Armor (which reduces speed to 20 ft - PC has 14 STR). I assume his speed should be 30 ft, but charsheet shows it as 20 ft. Am I getting it wrong?