Epona's real amount of usage definitely varies from Zelda title to Zelda title, and I feel this affects my feelings towards her. In Ocarina of Time - like we all know - you win her in a race and from there her use begins to decline. It unlocks the trade sequence for the Biggoron sword - which I liked - and makes it possible to get one of the empty bottles. Aside from that, her use in that game really just isn't too much. I liked how they introduced Epona's song and managed to keep it going throughout the Zelda titles with Epona in them.
In Majora's Mask, her use decreases even more. You lose her to Skull Kid - and he either kills her or sends her away - and you get her back - or Termina's Epona. From there you use her to get - yet again - an empty bottle when you help get rid of the alien invaders, gets you the Garo's Mask by winning it from the Gorman Brothers, and allows you to enter Great Bay. Now of course, you can continue using her if you feel the need to, but I've found the bunny hood - although slower - has a bit better turning than Epona does, and there is no wasted time while mounting/dismounting. In here, she is much like optional masks - she's there for your comfort, but you don't need her a great deal of the time.
Twilight Princess is where her usage really kicks in. You basically start the game with Epona, and you use her for wrangling goats, and many, many other important tasks in the game. Unlike in Ocarina of Time and Majora's Mask, there are multiple things that are required of Epona to continue the game. Whether it's fighting King Bulblin on the Eldin Bridge, or it's fighting Ganondorf on horseback, she is definitely needed. And one of the more interesting things is that she knows that you're wolf form is still you, and you can even talk to her while you're a wolf. Although she doesn't say much, it shows inteligence in her as an animal. In Twilight Princess, I didn't just feel like she was a small addition to the story, I felt like she was actually as important to the story as Ilia, or Rusl.