I'm not claiming this concept outlined below as a massively original idea. But perhaps the idea of "gentle" access to space is unusual?
What I'm talking about is a High-Altitude Platform (HAP), kept up with a very large amount of balloons, at an altitude of maybe 10 miles?
You could send all the bits of spaceship, and any payloads and people, up there by balloon, assemble the spaceship on the HAP and fly off slowly through the upper atmosphere. Only when you reached space would you start accelerating significantly, heading to the Moon for example. You wouldn't bother going into Earth orbit because that would involve too much acceleration. On the way back you would equally avoid orbit situations... and you would be using rocket motors to prevent you accelerating towards Earth (see below about fuel on the return from the Moon).
The final approach to the HAP on the way back would then involve decelerating through the upper atmosphere until you reach the HAP, where you would dock. Balloons would then be used to keep the spacecraft (and HAP) from falling to Earth.
People seem to be a bit confused about this idea of "escape velocity". The only thing you need to escape the gravitational well of a planet is to keep accelerating upwards with a slightly higher acceleration than the one in the opposite direction due to gravity: the velocity at any point is immaterial and both on the way out and on the way back could be low, low enough to avoid all the problems to do with atmospheric friction, and the imparting of huge acceleration forces to a vessel.
Starting off 10 miles above sea level, and travelling slowly through the atmosphere, would have lots of advantages from the design angle: your spaceship wouldn't have to be terribly aerodynamic in shape (because the velocity would be low and the air very thin), and it wouldn't have to have ablative heat shields. The amount of fuel saved by starting (and returning) slightly higher up might also be quite useful, if not dramatic (I've haven't tried to do any calculations).
Maybe such a HAP, and the spaceships, could even be made partly of wood? I love the idea of partly wooden spaceships, and wood as a material has some advantages over metal.
Just to answer the point about the possible gain from launching 10 miles up compared to sea level: JCRM says that space is big. True, but the bottom of a gravitational well is the worst place to start from, or to return to. This objection, if I may call it that, also assumes that there would be some big cost in maintaining this giant HAP 10 miles up in the sky, and in the launch and docking procedures. There would some cost... but not necessarily a prohibitive one.
Re the question of gravitational drag. I was vaguely aware of this. From a related question, as referenced by Hobbes, it would appear that it might be nice to position the HAP on the Equator and maybe to accelerate away with some lateral acceleration component (?). Nevertheless, the answer there with all the maths says that the gravity drag is significantly reduced by being just 5 miles above sea level. Not sure how all this works with returning...
Note about returning from the Moon
I described in a comment to the answer by Anthony X how you would use "juggling" (or "tacking" to use a maritime term) between the lunar and terrestrial gravitational fields to drag the spacecraft into lunar-terrestrial orbit and then land on the Moon. Leaving the Moon would be analogous: you launch into the direction of the orbital path of the Moon and cleverly use the combination of its gravity and that of Earth to slingshot you back behind the Moon, helping to take you out of (lunar-terrestrial) orbit. This makes you like a falling stone 250,000 miles above Earth.
You then need a full tank. With current re-entry, you use the air's friction to extract the energy from the craft's motion in terrestrial orbit, so you need only minimal fuel to return to Earth.
With my idea you need to refuel on the Moon. Impossible? No. There is water on the Moon. Water + electroysis using solar power --> (liquid) hydrogen and oxygen. You'll need pretty much the same amount of fuel to return as to leave Earth. Obviously in longer-term future you might want to take other fuel and chemicals from other parts of the solar system and transport them to the Moon.