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)?
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.
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