Depends; there are two ways to run a multi-monitor setup, depending on what video card you have and how it supports it. One mode is that it treats each display as its own desktop. Most games will not use the second (or third) display in this mode unless they are specifically coded for it (which some flight sims are; check the game's documentation). The second mode is to turn the 2/3 monitors into one giant desktop (at like 3100x768 or something like that), and if the game can support rendering at weird aspect ratios (which most recent games should), it will work properly. I believe NVIDIA and Matrox's software can do this, but I'm not sure about ATI's more recent drivers -- they didn't like a year ago, but they may have changed it since then.
You will need at least two video cards to run multiple monitors -- usually you'd get a dual head AGP card for two, and then add a PCI card for the third (you could also get an AGP card and two PCI cards, or even 3 PCI cards). Matrox *does* make a triple-headed AGP card, but its 3D performance leaves something to be desired (though it might be ok for flight sims). You also want them to be about the same performance-wise, as otherwise the last display won't be able to keep up.
Yes, it can be a big headache. Two's not so bad (but of course it useless for gaming), but 3 is real pain sometimes.