My last run-through, I was a warrior-type and I joined the Companions. As part of one of the quests, I got the fire breath shout. I don't think it's possible to complete that dungeon w/o the Companions (I'm really trying not to do any spoilers here). This time, I'm running a pure mage and wasn't planning on doing the Companions quests? I'm curious: Does this mean I won't be able to get all three words to Fire Breath?

Well if you don't do the quest then no unless you get it from somewhere else. I've done the same as you because being a warrior was so boring and so were the quests.

I'm pretty sure you can do that companions quest and then not pick up another quest if your concerned about unfinished journal entries, although you will forever be the mead fetcher or whatever the guards call you