Ask 10 people get 100 answers ;)
There is no right answer, I need more specifics (hardware, etc.) and I can guarantee that whatever the distribution says is the default is not good.
Generally partitions you want seperate are /var, /tmp and maybe /boot.
The reason for /tmp is that if you fill your tmp directory on its own partition, things get wierd and may fail but at least you can log in and fix it. THis is the reason Linux (in its infinite wisdom) has /root on its own psuedo partition so you can always (well almost always) login.
The same for /var as most logfiles are written there.
There are other issues such as security, multidisk setups, etc that need to be taken into account. In short there is no easy answer.
