Which one is the proper one to use?
For example, do I say “Can you give me that 25 foot cable?” or “Can you give me that 25 feet cable?”
Why would I use one and not the other?
First of all, it’s “25-foot cable.” Why? That’s an adjective, not a noun. You’re not talking about 25 feet OF cable, you’re talking about a cable. When you create a compound adjective this way, you use the singular form of the unit. Why? Because that’s the rule. It’s English, it doesn’t have to make sense.
I belive the correct way to say that is “Can you give me that twenty five foot cable, please?” 
Six feet tall sounds fairly kinky to me. :eek:
Actually there are lots of examples of this rule:
A six-foot-two man
A 120-pound woman
A 21-gun salute
A 2-liter container
A multi-level building
A 25-student classroom
A 6-cylinder car
A two-tone paint job
A 12-tone scale
A 3-ring circus
A multiple-choice test
A 90-degree angle
But some phrases get a “-ed” ending:
A 4-legged animal
A two-toed sloth
A 5-pointed star
And of course, a many-splendored thing
Each of these would sound really weird ending with an “s.”