Obviously with current rockets, it's necessary for that energy to be expended nearly all at once (8-12 minutes). But is that a law of nature or just a drawback of current technology? In other words, could you travel slowly into space?
This won't get you out of Earth orbit, though. If you want to go to other planets, you have no choice other than reaching escape velocity.
However, once in orbit, I'm pretty sure you can reach escape velocity as gradually as you want. You'd just gradually increase your orbit's apogee until you stop orbiting.
Also, the distances are so great that "travelling slowly" is not very convenient anyway.