I'm wondering if I complete the next main quest (in my case, the dragon killing quest in Whiterun), are then some other quests closed? I think, maybe someone dies who offered me a quest before... or something like this :)
The main quest "dependency" is in the civil war. If you choose one side, you can't finish up then rejoin the other side.
There are two types of quests within this game, pre-scripted quests and "random" quests. For example, asking the Riverwood barkeep for work will get you a pseudo-random quest, but working through the Companions line is fairly scripted.
I have yet to see a "random" quest direct you to kill off a questgiver, though the sheer number of possibilities will make this hard to prove unless a developer confirms it.
That said, if you go on a killing spree, be prepared for the consequences of your actions.