Why not have a craft go back and forth between inner and outer planets building up speed? Even if it took a hundred years, the final velocity would make traveling to another star time cost effective.
This isn't a complete answer, but there's practical limits to this approach. The planets likely wouldn't cooperate. http://en.wikipedia.org/wiki/Gravity_assist
The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example the Voyager missions which started in the late 1970s were made possible by the "Grand Tour" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.
Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the more boost it gets, because gravity falls off with the square of distance from a planet's center. If a spacecraft gets too far into the atmosphere, the energy lost to drag can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish aerobraking. There have also been theoretical proposals to use aerodynamic lift as the spacecraft flies through the atmosphere. This maneuver, called an aerogravity assist, could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.
In addition to this, the faster the spacecraft goes, the less of a push it gets from the planet and I'm not even sure back and forth gravity assists are even possible (well, maybe in a binary star system with 2 sets of orbiting planets).
In addition to userLTKs answer pointing out the lack of availability of planets there's another even bigger problem: Once you exceed solar escape velocity you're heading out no matter what. You can grab one last helping at the gravity assist buffet if anything is in your path but you can't turn back for more.