While on the quest for King Leoric's crown, I had to logout twice, each time after exploring a different crypt. Is it possible that the correct crypt has been rerolled, meaning that I have to explore again those two, or I can skip those and keep going on my quest?
Nicks answer confused me, so I just tested it:
Leaving the game doesn't leave anything intact, it resets your progress. To be more precise: You should look at playing Diablo III as playing a hosted session of a certain quest, with the bonus ability that quests transition into each other seamlessly. You can only start or resume the game from the beginning of a sub-quest within one of the main quests.
When you leave the game and then re-enter using the "Resume game" button, the gamestate is reset: The map is put back into a state where nothing is revealed, the random dungeons that appear on the overworld are shuffled again (this means that you can effectively farm a certain location until you've gone through all possible dungeons/events that can appear in that area), enemies respawn, etc.
If you simply "Leave Game", exiting to the hero screen, your game remains intact if you "Resume".
Relogging however, will completely remove your existing game; the "Resume Game" button simply creates a new game instance and drops you at the start of whichever zone.