Nine spacecraft have visited the planet Jupiter.  Here are simulations of their encounters with Jupiter.
Galileo went into orbit around Jupiter.  In the Galileo simulation, the spacecraft does not break into orbit, rather it continues on its hyperbolic trajectory.  Later, I'll add an orbit insertion burn when I can find the numbers.
 
The Galileo simulation also includes the atmospheric probe that impacted Jupiter
 
On the flyby simulations, after the flyby, center on the Sun, zoom out and watch the spacecraft continue to its destination planet.
 
Simulations
http://orbitsimulator.com/gravity/simulations/galileoJupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/newhorizonsJupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/cassiniJupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/pioneer10JupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/pioneer11JupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/voyager1JupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/voyager2JupiterApproach.gsim
http://orbitsimulator.com/gravity/simulations/ulyssesJupiterApproach.gsim
 
Screenshots (visible are Jupiter, Io, Europa, Ganymede, Callisto, and the spacecraft):
Galileo and its probe

 
New Horizons gets a gravity assist on its way to Pluto

 
Cassini gets a gravity assist on its way to Saturn

 
Pioneer 10 makes the first flyby ever of Jupiter

 
Pioneer 11's Jupiter flyby

 
Voyager I's Jupiter flyby

 
Voyager II's Jupiter flyby

 
Ulysses' Jupiter flyby