I know that in WOW, if you dont pick up quests, and start exploring, it usually means that you can't pick up an important quest/item loot, or you don't get credit. As a result the time can feel wasted.
Is there any danger in Skyrim of completing dungeons you happen to pass on the road?
No. But if you get a quest to go to the same dungeon that you would have went to without the quest, then you're getting more rewards.
A lot of quests are just to give you a reason/motivation to clear dungeons.