Speed limit in space agency is about 25 units per second. At this speed you have full velocity bar, and you can't accelerate using main engine (at least the standard way). But there are ways to travel faster than this:
Docking something with engines while thrusting somehow forces engine to stay active. (Thanks to Ad067612's research:) And because speed limit is bound to pressing the main engine button, you can gain post-limit velocity. Just make sure you aren't already traveling at post-limit speeds, because pressing that button will set your velocity at the limit. So if you want to gain some huge speeds, you have to refuel before your thrusting module runs out of fuel. Using this method you can have multiple engines running at the same time.
Thrusters are 2nd fastest way to gain post-limit velocity. Downside is, you have to constantly tap to gain speed, and it isn't most efficient way.Plus,with all the thruster fuel used up,you will not able to steer the vehicle anymore which is not very good
Oxygen Propulsion Edit
(More: Oxygen Propulsion)
Oxygen propulsion is most efficient way to travel in space. Speed is quite good and you have a seemingly very large supply of propellant. 2 seconds of oxygen propulsion is only as good as 1 tap on the thruster.
You probably are familiar with fact, that after un-docking you gain little bit of speed. It also works at post-limit velocity. Oxygen propulsion and this can move around about 3 module structures.
Fuel Leak Edit
It's most inefficient way to gain post-limit velocity, but most convenient. just open valve and you are done!
Gravity Assist Edit
You can run directly into a planet while avoiding the planet itself while going through the circle of influence inside which you can enter into an orbit.After you travel through the circle,your direction is changed to some degree and your velocity is increased.Just make sure you are initially going at escape velocity (speeds at the red bar of the meter) or you enter into an orbit around the planet.This method is tricky and unreliable as you may just rotate so fast after you get outside the circle,which may cause an explosion and destruction of your space craft,and it takes quite some experience to maneuver quickly enough at high speed that you will miss the planet but still go through the circle of influence which is a white circle around the planet.The closer your trajectory(the red line arising from your vehicle) is to the planet,the more acceleration it gets,in real life (haven't checked this out in the game)
Slowing down Edit
Gaining post-limit velocity is quite hard, slowing down is easy! Just start main engine and you are at the limit. (Actually, it's bit more tricky. I'm trying to figure it out.)
If you haven't any main engine, you have to slow down manually.