DIY Oscillosope probes
This is generally not a great idea. You're much better off making grab points for regular scope probes (making sure to provide nearby grab points for the ground clip, of course).

There are a number of problems, most of which you've actually considered - it's just that a direct coax connection is not the way to deal with them. 


  The signals may be in the MHz range (10-30MHz for example).
  
  I was thinking of standard 50-ohm coaxial cable, is there anything
  better?


Here's your first problem. 30 MHz signals will suffer visible degradation if they feed lengths of coax, unless the coax is terminated. Your signals will propagate to the scope, be reflected, then reflected again and distort the scope signal, etc. While it's worth keeping in mind that regular scope probes use lossy coax, this is not something you'll use successfully without a good deal of theory.


  Should I terminate it?


Oh, absolutely. If you do, you'll get excellent signals at the scope. Ummm. Well, there is the small matter of driving the cable, of course. For 50 ohm cable you need to provide a source which can successfully drive 50 ohms. This rules out all "normal" op amps and all "normal" logic circuits. It implies a series of high-speed, high-power amplifiers on your board which are only used when you hook your scope to the board, and for most circuits will represent a considerable increase in power dissipation - so you'll need bigger power supplies. But go ahead, by all means. 


  For 1:10 probing I thing a simple voltage divider is enough. Is that
  true?


Alas, no. While it's true that you could provide something like a 550/55 divider to produce a nominal 50 ohm source, when connected to a 50 ohm load you'd get about a divide by 20. Your circuit will see about 600 ohms loading, which is better than 50 ohms, but it's still outside the range most circuits are happy dealing with.


  How about capacitance compensation? How to generally reduce the
  capacitance of the probe?


It's true that this works for divide by 10 probes, but only with lossy coax. You might be tempted try an unterminated coax, but this will have a considerable capacitance (typically 25 pf/ft for RG58, for instance) loading of the circuit.

The only "good" way to do what you want is, as I've mentioned, install a 50-ohm driver amp at every point you want to monitor, then terminate the cable at the scope with 50 ohms. And that's probably not very good.