Are decoupling caps necessary for analog ICs (e.g. LM339, LM324...)?
In a mixed signal environment for production that has to pass FCC, yes absolutely.  

More specifically, what you need to do is look at your current usage, the frequencies that will be present, and determine what your overall power supply capacitance needs to be to minimize those frequencies on the supplies.  Otherwise you'll get ringing on the supply planes that can be a huge EMI issue.

You'll get some capacitance from the PCB stack up, assuming you have power and ground planes.  You'll then usually come up with a needed capacitance and size of capacitors to achieve your goal.  

For instance you can come up with something like:


30   0.1uF 0603 max
30   10nF 0402 to avoid lead inductance
5   10uF tantalum


Then sprinkle these around in a logical manner.  1 0.1uF and 1 10nF per power pin.  One tant per major IC or near a section of smaller current/analog ICs.

With mixed signal design you always have to remember that just because a signal is low frequency analog you still have to treat it as an EMI threat.  There will be transients from the rest of your system on that signal no matter how amazing your isolation is.  

Not only talking about high speed here either.  A system with a 25Mhz clock and easily have these issues and fail FCC pretty miserably (trust me :0)