Let me give you an example of where I'm at to start.
I just started practicing sus chords by ear
- Sus2 ascending chord is the same as Send in the Clowns.
- Sus4 ascending chord is the same as Final Fantasy Main Theme
Discoveries like this happen every time your ears begin to recognise new sounds.
I love Modes, and after spending time learning and playing the Lydian mode I began hearing it in songs where it's featured. The same with Mixolydian.
With Time signatures, learning how crotchets and dotted crotchets relate to each other mean unless there's something extra weird going on I can identify whether it's in 4/4, 7/8 etc, and even how the bar is subdivided. Having a developed ear for rhythm makes nightmares like this much easier to comprehend.
The Practical Value of ear training
When you train your ears you're lifting the bonnet on how sounds affect people. You're learning how to understand those sounds and subsequently, how you can use those sounds to affect people.
Just take a listen to Wagner's Tristan Und Isolde prelude. That opening chord has entire books written about it! If you developed your Ear to recognise that sound and how it's made, you could then not only reproduce it, but recognises places where you can utilise it yourself, which is an enormously powerful tool in your arsenal.
Incidentally the Tristan chord works by building to just before a note your ear expects, then playing a chord where the notes are just slightly off resolving, then doing it again and again.
Ted Greene talks about learning to recognise chords by ear and says
If you start to recognise the sound of nice chords when you hear them, you will also start being able to hear nice melodies or solo lines too.
He also says you will be able to anticipate the place that certain chord progressions are going.
John Petrucci said that Soloing is just getting the right balance of tension and resolution
as an extra from me. To do that you need good ears
How far can ear training improve your ears?
How long is a piece of string? in writing the Tristan chord Wagner pushed the boundaries of what was acceptable music at the time, and it took very well trained ears to know that he would be able to do that. Eventually when your ears are at the very limit of music that you listen to, they will go beyond that into something new.
How far can ear training improve your ears(alternate answer)?
It can improve your ears enough to take you next to a mountain, to chop it down with the edge of your hand.
It took all of the music that Hendrix listened to for him to create a new sound. All Hendrix relied on was his ears and intuition and it led him to Tritone intro and the Hendrix Chord used in Purple Haze
It allowed Robert Fripp to write The Court of the Crimson King.
Steve Vai said that your ears are the single most important thing to develop as a musician.
I hadn't really thought about just how far ear training can take you until you asked this directly, so thank you for that, but the real answer is that it can take you as far as you're willing to go. I'm learning to count advanced polyrhythms at the moment, but that's something that not everyone wants or needs to do.
Ok, let's take it down a notch, you can't as far as I know extend the frequency range of hearing for humans which is 20 to 20,000 Hertz depending on your age(wiki).
I believe the maximum number of voices you're able to perceive simultaneously is 9, so you couldn't transcribe most orchestral scores in one sitting, though you could probably get the overall harmony in most cases.
TLDR: It can take you at least as far as this