Of course, all dialogue should be dramatic dialogue. Boring dialogue should be cut.
Make sure to delete all but the briefest pleasantries and small talk - they're essential in real life; the kiss of death in fiction. However, although this dialogue needs to be dramatic, it absolutely must not be melodramatic.
Dramatic in this context means vibrant, involving conflict, involving change, involving movement. Good dialogue will have all of these things.
Melodramatic speech on the other hand would be overblown, unrealistic, clichéd, and sometimes even absurd. The dialogue would be exaggerated - way overblown for the occasion, and overly sentimental. You do not want that, of course.
If a scene is suitably dramatic, the reader will be affected by it - either sad, or scared, or exhilarated depending on the circumstances.
However, if the characters stoop to melodrama, it’ll turn readers off. It’s impossible to relate to.
So, have dramatic dialogue (exciting, vibrant, colourful, conflict-driven), not melodramatic dialogue (self-indulgent - on both the writer’s and the characters’ behalf).
Dramatic dialogue is where there is lots happening - but it's realistic, and the characters are reacting passionately but realistically.
An example of this might be:
"I'm afraid," John said, "that I've lost my job".
"Oh no!" said Mary, raising her hand to her mouth in shock. "That's awful. What on earth are we going to do?"
An example of melodramatic speech might be something like this:
"Oh Mary," John said, "I've some dreadful, awful news. Sit down dear, it's all going to come as a dreadful shock."
"What? What is it?" said Mary tremulously, sinking to the chair, her hand to her mouth.
"It's terrible. I don't know what we'll do. The fact is that I've lost my job."
"Oh no!" said Mary, gasping at the news. "That's awful. What on earth are we going to do? How will we survive? I don't believe it. Such a shock I can't tell you."
Do you see the difference? The melodramatic version is just overplayed and overblown. Think of it as hammy acting in print. It is also an example of purple prose.