The sad reality is that although computers and many scientific instruments have advanced tremendously in the last thirty years, basic propulsion technology really has not. A voyager-class mission, intended as a grand planetary tour, even if circumstances of the alignment of the outer planets were favorable (they no longer are for a Voyager type of mission) would take essentially as long now as then.
The current Cassini mission to Saturn is the last of the "big ticket" missions of exploration to the outer solar system. Two NASA administrators ago, a conscious decision was made -- many would argue wrongly -- to concentrate on many small single-purpose probes rather than general missions of discovery. Until that emphasis is reversed, it is unlikely that we will see any Cassini or Galileo type missions.
That said, one can still dream. Some scientists have proposed a probe that would orbit the Jupiter moon of Europa, and send a lander to sample the surface. Others have proposed a nuclear-based propulsion mission to send a heavy craft with many scientific instruments into Jupiter orbit to study its many moons, using the capabilities of the drive to adjust the orbit to make close passes to many of them. (Others claim this mission concept is given some funding merely as a cover to develop nuclear propulsion technology primarily for near-earth-space military purposes.)
A "fast and cheap" mission to Pluto has undergone several substantial reversionings -- a current one will probably launch in early 2006 (New Horizons) using, on some orbital scenarios, a boost through a Jupiter flyby.
This mission would gain velocity mainly through reduction in payload mass -- other more speedy routes to Pluto and beyond have been envisioned that would take a more circuitous route. Perhaps the fastest way to the outer solar system and beyond is actually a rather bizarre trick: sending a spacecraft towards Jupiter to do a "reverse boost" in speed, namely, to redirect the spacecraft into a close flyby of the Sun. The spacecraft would use the bulk of its onboard fuel during the flyby of the sun to accelerate. This change in speed would create a greater final velocity away from the sun than merely igniting the rocket motors in the near-Earth environment after launch.
Although several years would be spent in this initial odd orbital acrobatics, it's really the best way to maximize velocity and payload mass to the outer solar system with a given launch weight. At present, no scheduled missions are planned to use it, but one probably will eventually.