Do charged particles always travel in a spring shape around magnetic fields or only when the magnetic field is from a solenoid? I have seen two contradictory descriptions of how electrons  and other charged particles travel around magnetic fields; in one, they travel in circles around magnetic field lines, in the other, they travel in coil or spring-like paths around magnetic fields, with that said, which path do they actually travel when it's around a normal permanent magnet?
 A: 

If a charge moves into a magnetic field with direction perpendicular to the field, it will follow a circular path. The magnetic force, being perpendicular to the velocity, provides the centripetal force. 

If the momentum of the particle and the magnetic field line are perpendicular, then it is a circle. If there exists a momentum component in the direction of the magnetic field line, it is  a spiral . Both the circle and the spiral are affected by the ionization energy loss in the medium, the (projected in case of a spiral) circle radius getting smaller as the track lengthens
A: When the charged particle enters the magnetic field with it's velocity perpendicular to it then only the charged particle move on perfect circles or on a part of it till it is inside the magnetic field.
Now if the initial velocity of the particle is inclined with the magnetic field at some angle then the resultant motion of circular path and straight line will be seen(I.e. a helix or spiral shaped path) because now one component of the initial velocity will be perpendicular to it describing a circle and the other component will be along it so that the force of magnetic field is zero on it and the path of this component will be a straight line!
Hope you'll counter the question with this approach!
A: In the case the velocity of the charged particle is perpendicular to the external magnetic field. By this it's not important be this a permanent magnet or an electromagnet. After the electron leaves the magnet it's strength is unchanged. In the cas the velocity is not parallel to the magnetic field the path is a helical.
In both cases looking parallel to the magnetic field the path will be a spiral. This has to do with the emission of photons from the electron. The electrons kinetic energy gets "exhausted" by the photon emission and the electron at the end came to standstill.
A: The same path they would take around an electromagnet. They appear to spiral the wrong way, but if you imagine the pole being made up of a bundle of small poles, they are being pushed to the side where they are running parallel to the electrons around the atoms in the poles. If the magnetic field is above a critical level, they will be steered back in instead of spiraling out.
