Q:

Shapes of rockets on the Earth with no atmosphere

What would rockets look like if the Earth had no atmosphere?
How much easier would it be to launch satellites, and how much harder will it  be to launch returnable manned missions?

A:

Atmospheric drag and gravity losses account for about 1.5-2km/s of the normal 9.4-10km/s launch-to-LEO budget. 
With the trajectories we use, the atmospheric drag accounts for only a small portion of that, but we'd use more efficient trajectories and lower orbital altitudes if we didn't have to worry about the atmosphere! So at a guess, we'd need 8.5km/s instead of 10km/s of ∆v, which because of the nonlinear nature of the rocket equation, suggests you'd need only about 55-60% as much rocket for a given payload. 
However, the design of Earth-launched rockets is heavily constrained by the atmosphere. They're made tall and skinny to minimize drag, and have a streamlined skin around their tankage and payload, all of which adds weight. A rocket made to launch from a vacuum world would be made mostly of big spherical tanks attached to a minimal frame. The more compact shape would lead to a lot of miscellaneous weight savings -- shorter cable runs, propellant lines, etc -- which, while individually small, would add up. 
Launchers could use efficient, light-weight, low-pressure, liquid hydrogen fueled engines from the first stage, as well; system specific impulse gets better, rockets get lighter, everyone's happy. 
Return missions would be just brutal, though. In our manned missions, atmospheric braking provides essentially all the deceleration from orbital speed. Without the atmosphere, if you needed 8.5km/s to get up, you need 8.5km/s to get back down in one piece. To land a one man capsule like Mercury you might need to get something like 50 tons of payload into orbit!

A:

If Earth had no atmosphere I think you would see a far more radical change to spaceflight that the rocket redesigns other posters are talking about.  While rockets might have been used at the dawn of the space age I think we would be using something akin to maglev trains for launch.  Take a big flat area and put a very, very long track on it.  Unlike a train it would boost at rocket-type accelerations.  You boost your craft until it reaches the velocity of an orbit with perigee at 0 and apogee at the desired altitude.  The craft heads off into space, the train slows and is recovered.  When it reaches apogee it does a circularization burn.
If your accuracy is good enough you can even use a similar system to land--although I would do so with cables to grapple the returning spacecraft rather than attempting to actually dock with the train.

