What difficulty are you playing on for Strategy? The harder you have it there the more frequent the quests. Also, it really depends on what a race has going for it ie, the parameters for a quest need to be met obviously.

My experience with quests has been perfectly fine. Because I was at a point where races were at war with one another, a lot of the time there was bombing runs, ground invasion runs and quests to boost rci values. A lot of them pop up when there are wars, but sometimes you'll get a scientist wanting to defect with technology to you or a distress from freighters being harassed by pirates.

FYI this experience was on normal difficulty. If you try the hardest there will be lots of quests slapping you in the face in no time.

I won the game on normal, after giving all races spaceflight i "allied" with the Evuk and the Andor.

First i had to protect them a long time...then i had to stop the evuks from taking over all planets before i could form the real alliance :)

But...after the first two quests...i got not a single quest during the whole playthrough.