The honorifics I mean don't just refer to the ones used for addressing people, but also the way of speaking, etc. There are generally a few types of honorifics:

1) Talking to a superior (family or work)
2) Talking to a person of similar level
3) Talking to a person of lower level
4) Humbling sentences, meant for politeness

It's not just about adding -san to a name for respect, but your entire sentence structure can change.

Simple example:

"Can I borrow a book?"

To a person of same/lower level: "Hon o kashitte mo ii?"
To show politeness : "Hon o kashitte mo ii desu ka?"
To show respect: "Hon o kashitte kuremasen ka?"

This is just a very simple example, and there are much more complex forms for other verbs, such as eat:

"Have you eaten?"

normal: "Tabemashita ka?"
honorific: "Meshi agarimashita ka?"

And this is just the tip of the ice berg, as the Japanese practices very different style of speech to different audiences. Most of the time, the words you hear in anime belong to the more impolite category, and my sensei used to tell us to avoid some of the terms which I thought were part of everyday language.