As far as I know (which isn’t as far as it gets), using -desu as a suffix when speaking Japanese would show a bit of courtesy in a sentence. Well, anime would tend to over-exaggerate that, with some characters overusing the suffix. Even some speak basically useless words affixed at the end of their sentences to show some sort of cuteness in speech.
So here are some examples of anime characters saying different kinds of suffixing in their dialogue. The intensity part basically suggests how much they use the suffix.
Yue (Mahou Sensei Negima)
suffix: -desu
intensity: medium
Chisa (Comic Party Revolution)
suffix: -desu
intensity: medium
Sabato (Bokusatsu Tenshi Dokuro-chan)
suffix: -desu
intensity: high
Tamami (Mahoraba ~Heartful Days~)
suffix: -desu
intensity: high
Kaede (Mahou Sensei Negima)
suffix: -de gozaru
intensity: high
Subaru (Comic Party Revolution)
suffix: -desu no
intensity: high
Pumo (Futago Hime)
suffix: -pumo (doesn’t mean anything)
intensity: extreme