I have recently read an article about gravitation slingshot assist used by Voyagers 1-2, and was thinking on why this hasn't been used for travel between solar and other systems.
I mean sligshot can be done as many times as it is necessary to get speed of lets say half the speed of light that would allow to travel to Alpha Centauri in ~10-20 years can it not? There must be a flaw in my thinking that 3 or 4 planets can be re-used to get to necessary speed otherwise it would already have been done (drawing below). Even if planets would align differently I should always be able 'find' the planet that would allow me to jump to one that is closer to the sun, and repeat the acceleration again and again. 
What maximum (theoretical) speed could be achieved using planets of solar system as sligshot and how much would this speed wary from planetary alignment and what realistic speed could be achieved?
UPDATE: To be more specific on the second part of the question Lets say craft weight's 500kg at starting speed of 30,000 km/h initially it slings around Mercury (radius 2440km), Venus (radius 6052 - 300 (atmosphere) = 5750 km), and Earth (radius 6378 - 300(atmosphere) = 6050km) until diameter of planets is to wide to not to crash craft on surface. Then it flies to the moons of Saturn - Titan (radius 5150km), Rhea (1527km), Lapetus (1470km), Dione (1123km), Tethys (1062km), Enceladus(504km), Mimas (396km) and starts slinging there until diameter is to wide too. What approximate maximum speed could it get to leave the solar system?
Answer
One can get an order of magnitude estimate of the maximum speed attainable by gravitational slingshots without doing any real calculation.
The 'rough physics' reasoning goes as follows:
The gravitational field of the planets used for slingshots needs to be strong enough to "grab" the speeding spaceship. As a planet cannot "grab" a spaceships moving faster than the planet's escape velocity, it is impossible to slingshot a spaceship to speeds beyond the planetary escape velocities.
So no matter how often our solar's system planets line up and no matter how often you manage to pull off a perfect gravitational slingshot, you are practically limited to speeds not exceeding roughly the maximum escape velocity in the solar system (i.e. 80 km/s or 0.027 % of the speed of light, the escape velocity of Jupiter).
(Note: by working with well-defined trajectories one can refine the above argument and get all the numerical factors correct.)
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