Archmage Trebonius of the Imperial Mages Guild will eventually ask you to kill all the Telvanni Councilors. For obvious reasons, this is not particularly helpful if you want to go down the Telvanni questline. That said, it's relatively easy to replace Trebonius before he can offer you this quest, and you can replace him even if he's already tasked you with killing the Telvanni Councilors, which will essentially invalidate the quest.

The Temple has a quest for you to kill off the leadership of the Berne vampire clan, so if you want to do the Berne vampire clan quests, take care of them before getting (or completing) the Temple quest to kill Raxle Berne.

House Telvanni has a retrieval quest for vampire characters which can conflict with a vampire clan quest for Berne clan vampires, and will send you to the ruin in which the Quarra clan leadership resides.

You can only join one of the three vampire clans; which one depends on what kind of vampire 'sired' you. The second (and last) clan quest in each vampire clan's questline also asks you to kill a bunch of vampires of the other two clans.

Won't break things, but the Morag Tong can get somewhat irritable if you kill someone before being given a writ to kill them. Late in the Thieves' Guild questline, there's a quest to kill two people for whom the Morag Tong has writs.

Some of the earlier Morag Tong writs send you out to kill relatively unimportant members of each of the Great Houses, which could get you expelled from a Great House if you're not at least slightly careful.

The Morag Tong's post-Nerevarine quests involve assassinating high ranking members of the Imperial Legion as well, I think.
The Grandmaster Writs send you to kill one legion commander, one Hlaalu councilor, one Telvanni councilor, and a wizard in Gnisis.