I generally find it helpful to think of them as overlapping effects as opposed to stacking. Sometimes, as mentioned by @lizardggY, receiving the same condition multiple times will advance you along the condition path. In those cases it will be explicitly stated in the condition/power/feat/ability/spell/dance/jiggle.
So in your situation the shaken condition does not specify that multiple shaken conditions advance you to panicked. Nor does the panicked condition state that you can receive the condition from having multiple instances of shaken. Bit of belt and suspenders reasoning there, but still worth checking.
Duration and abilities that remove spell affects are where it becomes necessary to track each individually. So the description of Intimidate(Demoralize) states that the duration is 1 round, plus some more if you beat the DC well enough). Let's assume you do really stinking well and the duration is 3 rounds. The Doom spell has a duration of 1 minute per level, let's assume minimum caster level so 1 minute or 10 rounds.
In this situation you are under the affects of both Demoralize and Doom. Since they both produce the same affect you suffer from the standard Shaken penalties. Three rounds later the Demoralize wears off and you lose an instance of the Shaken condition. You still have 7 rounds of Doom, which means you are still Shaken.
Alternatively, let's assume in round 2 you are blessed with a Dispel Magic and your castor makes the check. This removes the Doom, however due to Demoralize you are still Shaken for one more round.
This is why it is always important to maintain your list of all affects, and sources, even if they produce the same condition.