I guess it depends on what is going on in the story, but I think that in real life every experience changes you, even if it's only slightly, so it would seem unrealistic for a character to pass through the events that make up a novel without having changed at all.
I agree. Not every character change is profoundly obvious. This is also very realistic. In reality, when your girlfriend leaves because you are a slob, or your boyfriend leaves because you are emotionally cold, do we, as real people actually have after-school-special epiphanies?
Also, one of the major themes in Neon genesis Evangelion is a very interesting philosophical point - 50% of us is how others perceive us. The average free-thinker (myself included) is reluctant to accept this, but look at it this way:
You step into the elevator. A woman begins to step in after you, looks you up and down, and then visibly chooses not to get into the elevator.
This affects you, whether you want it to or not. The effect is different depending on each of our circumstances. Maybe you are dripping grime and she has on a Vera Wang, maybe she's racially motivated, maybe you're a stalker. Either way, that moment has some ramification on how you finish out that day. Maybe you lose your mind, maybe you never tell anyone, but in the end, you are affected.
Life is a long stream of actions, reactions of others, and then your reaction to those reactions--and no reaction is, in fact, a reaction, often one of the strongest.
Characters that change subtly are difficult to render. The author must have a more fine control to stop them from being boring, or getting the "stagnant" label or poorly developed label. Honestly, many well-developed characters (i.e. Holden Caufield, Gatsby, O'Brien in 1984) don't change much, if at all, but their lack of change is kindof the point.
Also, becoming dead is a change, and it happens to many characters who refuse to change with their environment.