To start it off, a technical note, a single Decider Combinator set to "=0" is a nor gate. If you know your circuit logic, you'll realise that means deciders, all by themselves, are logically complete. Now, you could make logic gates before, using smart inserters, but such systems tended to be slow and clunky; no more!
Friday Facts #88 showed us a simple timer using combinators, but that's just the tip of the iceberg.
With a Decider being a nor gate, just 2 of them can make a compact and reliable S-R latch...
Those make a basis for any number of other practical systems.
On a whim, I decided to set up a 7-segment decoder, that displays the number of items in a chest. I used... quite a few combinators (93, to be exact, though I'm sure it could be optimized considerably) but it was just a proof-of-concept. It refreshes almost instantly to any change in the quantity in the chest. I only gave it 3 digits, but it's scalable, and you could expand it to as many digits as you liked easily.
(forgive the ugliness, it's not a polished installation in a real build, just a proof-of-concept in a test world)