If traveling to distant planets in less time is an issue because of the fuel or speed, why can't we make use of a planet's magnetic field to accelerate ourselves given that almost all planets in our solar system have their own magnetic field?
Are they too weak?
At the distances involved, a magnetic field is much weaker than a gravitational field. So instead of using the magnetic force, we use gravity (i.e. gravity assists) to accelerate interplanetary spacecraft.
The Earth's magnetic field is far too weak to provide much force to a spacecraft. At LEO the earth's magnetic field is probably somewhere around 50 microteslas, or 50,000 nanoteslas (it varies greatly by your position above the Earth) in intensity.
The Earth's field ranges between approximately 25,000 and 65,000 nT (0.25–0.65 G). By comparison, a strong refrigerator magnet has a field of about 10,000,000 nanoteslas (100 G).
So a refrigerator magnet is 200 times more powerful than the Earth's magnetic field. In order to convert this force to movement you'd need to interact with the earth's magnetic field with an incredibly powerful magnet field which your spacecraft would have to generate. This would be 1) very heavy and 2) the magnetic field would be hazardous to people and equipment on board. Even with a massively powerful magnetic field on a spacecraft you would not get much propulsion out of it due to the earth's weak field.
Lastly, magnetic fields quickly reduce in strength the farther away you get from the source, meaning you would need another form or propulsion for course corrections.
The two previous answers correctly state that magnetic fields are too weak at planetary distances. The reason for this is that, roughly speaking, the magnetic field's intensity is inversely proportional to the third power of the distance. In contrast, the gravitational field's intensity depends only on the second power of the distance.
Thus, to make use of planetary or solar magnetic fields, one would have to put much effort into generating electric currents. The corresponding increase in mass and energy consumption would not be worth it, i.e. carrying more fuel instead would be more beneficial.
There are proposals and have been experiments towards using Earth's magnetic field to (slowly) adjust the orbits of satellites. See this Wikipedia article for instance. Since the satellites are orbiting within the magnetic field for long periods, even a gentle thrust adds up over time to make a useful change in orbit using electrical power, but crucially no reaction mass.
Some satellites do use "magnetotorquers" to maintain attitude, so they use Earth's magnetic field to rotate themselves.
