* you forget to ground a particular node, or
This is one that can sometimes help: it's rarely a good idea in actual practice to leave nodes floating. SPICE specifically forbids it -- it will generate a "singular matrix" error, which is to say, it can't find a solution for some set of nodes (e.g., series capacitors) or loops (parallel inductors) because there is an excess degree of freedom in the equations (the voltage on the floating node(s), or the current in the loop, could be anything, so when it tries to find *one* solution, it fails).
But this, too, can be gummed up. Typically one sets RSHUNT = 1e9 or so, which is usually enough to "bleed" floating nodes towards ground. But the simulation crawls slowly (the matrix is near-singular, forcing it to do extra work) and you don't know why, until you spot the mistake. As usual, there is no substitute for a vigilant eye.
In general, a more physically realistic circuit is also better to simulate (besides producing more realistic results). Wires have inductance. Nodes have capacitance. Inductors have resistance (series and parallel -- both dependent on frequency of course..). Capacitors have ESR and ESL. It can be helpful, for instance, to take a diode model (typically, manufacturers provide just the .MODEL for diodes, which only represents a certain ideal approximation of the die alone) and pack it in a SUBCKT with realistic package parasitics (I usually go for series lead inductance, in parallel with a damping resistance, and a small capacitor across the diode to aid convergence -- wide swings in circuit parameters, like CJO, make for slower simulations too).
Your overall model is only as good as the sub-models in it; scrutinize them well. One of the most notorious types are the three-terminal op-amps -- without supply rails to work from, they simply produce an output corresponding to the input stimulus, no clipping whatsoever. 40kV from a "LM741" seems strange, but it's quite logical for a three-terminal model. Such models may not include slew rate limiting either, so beware, not just of nonlinearities, but also their potential absence -- which, of course, unless you're familiar with the device, you won't know offhand whether it's right or wrong. Confusing business for a beginner.
One thing I've had trouble with is getting good switching behavior out of a MOSFET. Some models consider Cdss, some don't. The problem is, when the MOSFET turns off, that capacitance has to be charged, and how fast it charges strongly controls how much power is dissipated in the transistor. So, you can set up a toy simulation where the MOSFET switches a current source; when it turns off, drain voltage rises proportionally to the capacitance. Often, they'll be lazy and put in a constant capacitance. This is pretty awful when you consider the datasheet says the capacitance varies from 10nF from under 10V, to less than 500pF at 100V -- a huge difference! Or they'll miss breakdown voltage, so over time, the voltage just keeps on rising happily -- 10kV on a 500V device, anyone? Some of these are easy to fix by hand (add BV and IBV parameters to the body diode model), others not so much (good luck fitting some of the more extreme capacitance curves). Sometimes the datasheets even lie -- I have one example of an ST transistor which I measured the Cdss of; the datasheet graph is significantly steeper than the real article.
On the other hand, some manufacturers go to great lengths to provide accuracy; I believe it was an Infineon model I once tried, which was, sadly, completely useless to me -- it ran too slow to get numbers out of! I don't doubt the accuracy of their model, but there is ultimately a speed-accuracy tradeoff which one must consider in the process. And that includes how broad a range a model covers. This particular example, I went with a similar Vishay/IR device (which uses a Level 3 MOSFET model; average quality) and did the boring usual engineering process: overestimate losses as a worst-case, and optimize to that, so that the real thing probably works much better than, but hopefully no worse than, the model.
Things that -- alas -- you can do on paper anyway, with the understanding that, hey, you're doing it on paper, so of course the numbers are going to suck -- so you overestimate by a moderate factor, and it probably works first time. One would hope simulators can avail us of such process, but that is not the case.
Tim