"Keep on hand" in the sense of having with you whenever you shoot?
Definitely the slide lock spring. If that breaks, the slide may fall off or fly off, and they DO rarely break or lose tension. (I've had one lose tension on a G21 and one actually break on a 9mm, a G26 IIRC.)
If the trigger spring breaks, the gun still functions, but it's easy to carry spares.
Never heard of any Glock recoil springs, striker springs, extractor depressor plunger springs or slide release springs breaking. Since the recoil, extractor and striker springs operate in compression, it would be quite unusual for any of those to break.
Standard trigger springs and locking blocks do break, apparently, though I've never had it happen personally, in any caliber. (I own 9mm and 45ACP Glocks, and used to have .40 S&Ws too, but got rid of them.)
I've had two complete sets of G19 parts (everything but frame, slide and barrel) plus numerous "extras" like slide lock and trigger springs (standard, NY1 and NY2), the various pins, and much other stuff, since 1999, as well as multiple other spare parts for G21, G30, G36 and G26 models, and have never needed ANY of 'em except for a couple slide lock springs.
I do change recoil springs, standard trigger springs and striker springs as well as magazine springs at regular intervals, with Wolff items, just "to be sure", but it's probably an over-abundance of caution on my part. (I did definitely have some Glock OEM G23 magazine springs poop out completely once upon a time, though, so that the gun wouldn't feed a single round.)
"Therefore, since the world has still... Much good, but much less good than ill,
And while the sun and moon endure, Luck's a chance, but trouble's sure,
I'd face it as a wise man would, And train for ill and not for good." -- A.E. Housman
I will likely have it all with me, its primary purpose is to keep the gun running. I shoot a few Glock shoots a year so the gun will be gone through a couple times by them as well.
You could, honestly, carry every replacement part in an Altoid can... So, why not?
I carry one of each spare part to the range, conveniently packed inside a slide and frame.
My Glock parts/sight tools/trigger pull gauge/targets/ammunition/ are in my vehicle daily. Being retired I often work on Glocks for others on short notice which is sometimes done on the tailgate of my truck and I am always prepared for a range trip.
I know it's snarky but this is what I was thinking.
Eta: if a part can break and stop the gun from working, it is by definition a critical spare. To that end I would think everything short of the barrel, frame, and slide would be a critical spare. At that point a spare gun would prevent having to wrench at the range, along with being easy to store and keep organized. Just my .02
Sent from my iPhone, I apologize in advance for typos.
"Gustatus similis pullus"