Although a lot of tools exist, the two primary forms of simulation are analog (SPICE, LTSPICE or Simetrix for example) and signal integrity (with something like Hyperlynx if you have very deep pockets).
There are power analysis tools, but I have seen some very odd results that do not apparently equate with physical reality.
There are mixed signal tools, although the digital side tends to be behavioural.
The problems we run up against are:
1 No simulation model exists for the part. If you have a complete datasheet you can make a decent stab at rolling your own or use a part that does have a model.
Rolling your own model for anything non-trivial is a very time consuming exercise.
Note that anything beyond a primitive (diode, transistor or simple passive) is a behavioural model that reflects device operation in the continuous state. See this application note for what is actually in such a model. Note that things like ferrites and chokes are very complex; although they can be modeled as a circuit (to achieve the response in the datasheet) it can be very time consuming.
2 Run time. I simulated the entire power path for an ejection seat to include the EEDs and thermal batteries as part of an independent safety review of the sequencer electronics. As the cables to the control and firing circuits were quite long, they were modeled as loosely coupled transformer windings. The circuit contained perhaps 40 elements and took (on a multi-core high end machine) over 30 hours to do a single transient run.
3 Some parts of the circuitry are not really suitable for simulation or should not need it. If I have a simple optocoupled isolation stage to toggle a control switch, it should not need simulation if the data sheets have been used properly (of course, that is a completely different subject as I have seen many designs where that was not the case).
4 In Signal Integrity simulation, most simulators do not take into account that controlled impedances are +/-10% at best, and will vary layer to layer. Such simulations are useful to see gross issues, but you can still get bitten by such details. In addition, most simulators cannot model the return path (although post layout simulations are getting better).
5 Virtually all simulation models are compromises to reflect the most common use case; I have had to modify models significantly to see corner case behaviour.
A full board (or often multi-board) system would be prohibitive in terms of time to actually run, so only the parts we are interested in checking are simulated.
Another issue is that for macro-models, start-up behaviour is undefined in many cases and no simulator in the world will help if start-up behaviour is critical (as it can be in flight safety critical equipment) - you simply have to measure it.
Simulations can certainly help designers, but they are not anywhere close to perfect and should not be relied on for actual circuit operation; they are indicative of circuit operation.