Here is a small tutorial on RC networks, explaining the disfunctions of our precious embedded designs such reset circuits can cause. The following lines are from a response I got from KW (I contacted him for suggesting me reset/supervisory chips for my application), engineer in the Supervisors & NV-RAM Controllers Maxim's department, which I thank him very much for all the time he spent for explaining me in detail why we should avoid using RC networks and instead use reset/supervisory chips. So let's go:

"Using a discrete, RC circuit to reset a microcontroller is generally a
risky alternative. A number of problems beckon when you use that approach.
First, many processor reset inputs require a logic signal whose rise and
fall times are sufficiently short - something that a long-time-constant R/C
circuit cannot provide. But if the processor's reset input includes a
Schmitt trigger, the reset input should be able to tolerate signals with
longer rise and fall times. You can add a Schmitt trigger between the R/C
and the processor's reset input, but the Schmitt trigger can also contribute
startup problems as well as consume board space and add cost. The longer
rise time of an R/C also creates a possible problem for those processors
with a bi-directional reset pin: the processor could misinterpret whether
the reset was internally or externally generated if an R/C is used.

A second problem arises when a discrete POR is used along with a supply
that, when powering up, rises slowly in relation to the POR's time constant.
The POR's voltage can reach the minimum VIH of a processor's /RESET input
prior to the supply voltage reaching the minimum specified voltage at which
the processor is guaranteed to operate correctly. Thus the processor can
come out of reset well before it has stabilized. You can appreciate how
this could happen when you consider that the minimum VIH for most processors
is 0.7VCC while the minimum guaranteed operating voltage for many processors
is 0.9VCC. To prevent this problem, you may need to increase the time
constant of the R/C circuit. Some manufacturers whose processors include an
internal POR recommend that you add an R/C (plus a diode whose function is
described below) to the reset input if the power supply comes up slowly.

After power up, if the power supply glitches or droops below its specified
range, a third problem can arise when a discrete POR is used. The R/C
circuit filters out quick glitches, thereby preventing a reset from
occurring even though the glitch may have corrupted the processor's internal
registers. Also, if the supply droops, the voltage at the processor's reset
pin could remain too high for a reset to occur (it has to reach VIL min.),
even though the supply has dropped below the processor's minimum guaranteed
operating voltage. Furthermore, if you turn the power off and then on again
quickly, the capacitor may not have had a chance to completely discharge
prior to the power coming back up. Thus the processor might not recognize
the resulting signal as a reset.

You can improve the R/C circuit by adding a diode. With the diode added, the
circuit can now respond to glitches because the diode quickly discharges the
capacitor whenever a glitch appears. This technique can only work, however,
if the glitch voltage is large enough to drop the voltage at the diode's
cathode to a diode drop below the VIL min. of the processor's reset input.
Thus, a glitch could readily upset the registers within the processor
without initiating a reset. Plus the other problems listed above for the
R/C circuit without the diode can potentially plague this circuit, too,
although the diode does, in some cases, fix the problem created when the
supply is quickly cycled off and on. Furthermore, an R/C circuit comprises
two components (or three when the diode is used), whereas an integrated POR
is one; those extra components entail additional assembly time and
reliability concerns."