Many people have a rather amusing concept of what "escape velocity" means. When talking about the escape velocity of the Earth, they seem to think that an object cannot leave Earth unless it reaches that minimum velocity. This notion is so engraved in many people's minds that I have even seen someone asking this type of question at a physics forum:
"I don't understand this escape velocity thing. If I just lifted and lifted an object until it's outside of the Earth's gravity influence, without ever even approaching escape velocity, what would stop me?"
This person showed a great deal of independent and scientifical thinking, and his question is very valid, which is absolutely commendable. However, this question shows us how badly he had understood the very concept of escape velocity (either by it being taught wrongly, or him not understanding it correctly).
Many people seem to think that escape velocity is some kind of magical barrier around the Earth which cannot be bypassed by anything moving at a velocity smaller than the Magical Escape Velocity. Even though they may not word it like that, how they talk about it sounds exactly like that. If they are asked about the apparent contradiction that this idea imposes, they just don't know what to answer.
Of course that kind of notion is nonsense. There is absolutely nothing stopping an object from leaving Earth at any desired speed. There's no magical barrier.
What escape velocity does tell is the initial velocity that an object must have in order to escape to infinity from the surface of the Earth, assuming that the Earth would be the only object in the Universe (besides the object to be launched) and would have no atmosphere (which would slow down the launched object). In other words, if no additional forces are applied to the launched object after it has been given its initial velocity, escape velocity is the minimum initial velocity needed for it to escape to infinity (never returning to Earth).
There's nothing stopping an object from leaving Earth at lower velocities if it has a constant thrust which takes it out. The concept of escape velocity is not related to thrust, only to initial velocity (followed by not applying any additional forces to the launched object).
Also another important thing to understand is that escape velocity depends, naturally, on the distance from which the object is launched with respect to the planet's center. The higher the object is to begin with, the lesser its escape velocity will be. These are important concept when calculating orbits and trajectories and such.
The misconception might be partially enhanced by the fact that space rockets launched from the Earth try to achieve escape velocity. However, this is not because it would be impossible to leave the Earth otherwise, but because it's the most fuel-economical way of leaving the Earth (ie. less fuel is required to reach escape velocity and then just let the rocket go, than it would be to try to leave the Earth at a lower velocity, which would require a prohibitively longer thrust).
Note that Earth's escape velocity is enough to leave the Earth... assuming there's nothing else in the Universe. Since the Earth is not alone, it's not actually possible to go to infinity from the Earth by reaching Earth's escape velocity (which is about 11.2 km/s). In order to leave the Solar System (from the altitude of the Earth) an escape velocity of 42.1 km/s is needed.
(And again: Escape velocity here refers to an initial impulse after which the launched object is left alone, without any additional thrusts. Of course an object could leave the Solar System at a lower velocity if it had constant thrust, but that would be prohibitive fuel-wise.)