Why do rockets accelerate fastest horizontally? I've heard that rockets accelerate fastest when travelling horizontally to the ground, not downwards or upwards. Is that true, and why?
 A: Rory Alsop explained why the idea is wrong, but it may originated from the following reasoning.
When a space rocket takes of, it does so vertically. At that time it is fully loaded with fuel and hence its acceleration is slow. When you watch a video of a space rocket take-off, it seems to crawl along the launch tower.
However, in order to achieve orbit, the rocket has to travel 7 km/sec horizontally. To achieve that, after a while the rocket's path starts to curve towards the horizontal. At that point the first stage may already have dropped off and a large amount of fuel has been burned, so the rocket is a lot lighter. Because the acceleration is inversely proportional to the mass the rocket will be accelerating significantly faster at that point. At the same time, because the rocket is now fairly high up, the air pressure has dropped significantly, and the reduced drag also increases acceleration. 
Hence, the rocket accelerates faster when it is going horizontally. Somebody could then take that as meaning "faster than upwards as well as downwards"
Edit
Another issue is the is the "dynamic pressure" which is created by the speed and air-drag. Because of this, the engines may not be run at full power until past the "max-q" point. In the case of the Shuttle, the main engines ran at 65% for the first minute or so of the flight. Only then was it throttled up to 100%, increasing acceleration. See http://www.aerospaceweb.org/question/aerodynamics/q0025.shtml
A: Pretty straightforward, really:


*

*Accelerating upwards, the rocket can accelerate at T-g, where T is thrust, and g is the acceleration due to Earth's gravity.

*Accelerating downwards, the rocket can accelerate at T+g

*Accelerating horizontally, the acceleration will be T


So you can see that it will accelerate fastest downwards.
A: To move from one orbit to an orbit that is further out you want to add energy to your rocket.  This is most efficiently done by adding thrust in the direction you are traveling.
Furthermore, in a Hohmann transfer you are making two burns.  - When increasing your orbital radius this is one burn to raise your apoapsis, and one burn to raise your periapsis.  The most efficient way to raise your apoapsis is to burn at periapsis, and the most efficient way to raise your periapsis is to burn at apoapsis.  On both periapsis and apoapsis your trajectory is parallel to the ground, and so you get the highest efficiency when accelerating horizontally.
A: Less Air Resistance, and there is gravity which prevents not only prevents the rocket from moving quickly but also slows it at down (at about 9.8 meters per second squared). 
