astrophysicsmagnetic fieldsplanets
In this Wikipedia article it is stated, that magnetic field of Earth is caused by currents in her core. The same origin is for Jupiter magnetic field.
For Moon (article) there is a magnetic field, but having other origin than the Earth's one, perhaps Uranus too.
Are there any other planets that we know for sure they have no magnetic field (or perhaps it should be considered as none) or are we sure that all such bodies must have magnetic field (why then)?
The gravitational potential energy of a polytropic sphere of gas (i..e governed by a polytropic equation of state), with a polytropic index $n$ is given by $$ \Omega = -\frac{3}{5-n}\ \frac{GM^2}{R}$$ See for example here.
A constant density sphere would have to have to be incompressible. Since a polytrope has a pressure $p \propto \rho^{1 +1/n}$, this corresponds to $n=0$ and gives you your result for a uniform sphere.
Higher values of $n$ have more centrally condensed profiles and larger binding energies.
The appropriate value of the polytropic index for brown dwarfs and gas giants, where energy transport is convective or where the gas is (non-relativistically) degenerate is $n=3/2$. In which case, your leading coefficient increases from 3/5 to 6/7. i.e. No big deal for an approximate calculation.
After all, an object which is not gravitationally bound to another object will never become gravitationally bound unless it interacts with other objects so it can shed some of its energy.
This is true, but you've forgotten about the Sun. Every interaction between a planetismal and Jupiter is a three-body interaction.
Above, a simulation of a low-mass planetismal moving in the effective potential in the rotating frame for a planet with mass $10^{-3}$ of its star's mass. The Lagrange points are marked with $\color{orange}{\times}$. The particle starts at $%(0.83,0.47)$ some random place I clicked; it moves ahead of the planet for two or three orbits, pausing at a couple of unstable stationary points in the rotating frame, then has a close interaction with the planet. In this case the close interaction doesn't lead to a capture, but you can see from the inset that the interaction is chaotic: it's extremely sensitive to the details of the closest approach. You can surely imagine a three-body interaction that ended in the particle being captured by the planet, even if I haven't hunted for one to show you.
Best Answer
Our two closest planetary neighbors -- Venus and Mars -- have no significant magnetic fields. In fact, the most recent numbers I know of for an Earth-like (dipole) field on Mars say that its strength as no more than 1/10,000th the strength of Earth's. On the other hand, Jupiter's magnetic field is about 20,000 times stronger than ours.
There is no reason that planets should necessarily have magnetic fields. However, since most planets (and moons and stars) are believed to be formed in processes that involve lots of angular momentum, they will mostly tend to have lots of rotation, which will tend to create strong magnetic fields.
On the other hand, there are processes where the magnetic field can die away. In fact, there are bands of magnetic field on Mars, which suggests that Mars once had a much stronger field, like Earth's. You can see an article about that here.
To summarize: there's no reason to expect lots or little magnetism.