I would disagree with Ember on the first point. To me, a tremble is gentler than a quiver. It also suggests a lower frequency to me - it's more of a shake. I think that although 'tremble' is the more common and normal word to use with fear, quiver and to some degree shiver would also both work.

Tremble with fear. <-- bigger? Quiver in anticipation.<-- smaller Horror makes a shiver go down my spine. <-- small and short-lived?

you could say that tremble is a more powerful shake than quiver. when someone says quiver it seems like a little shake, while trembling; ex. trembling in fear- is almost a violent shake. if you use the word shiver, it usually implies that one is cold, and that would not be the proper use in the situation.