I have Quest Helper for this.
I'm not always happy with QH, but it will say how many my current toon needs of whatever.
And how many party members are totally done, and how many are in progress.
This is the quest progress section on my UI.

In the case of a drop from a mob.
Mousing over the mob will show me a progress of each of my toons.

In the case of something to be looted or a ground spawn.
It functions the same as the mob, mouse over for a progress for each toon.

I like the arrow which gives a direction to complete the quest.
It sucks at times, because it is as the crow flies.
And that doesn't always work in classic wow.
But once you get to Outland/Northrend, a directional arrow is pretty decent.
The Blizzard quest integration into the map is more reliable.

But as far as tracking quests goes, QH definitely is an option.