Here are several points that might help you:
1. In general, provinces rebel when loyalty gets too low. Anything below 100% is in the danger zone, although I think that factions can re-emerge in territories where loyalty is under 120%. As a matter of preference, I try to keep loyalty above 150% if possible.
2. Use the SHIFT key to quickly check loyalty levels in your provinces. Any yellow or red provinces might cause you problems in the future - do something about them before they revolt.
3. Tax levels have a lot to do with loyalty. In vanilla MTW, auto-tax tries to keep loyalty at 100%. This is risky, since many events can cause sudden loyalty drops, so I manage taxes myself. Once you have a huge empire, you can usually afford to leave taxes at a low level in most of your provinces; just raise taxes in your rich lands and make sure they are properly garrisoned.
4. Religion has a lot to do with loyalty. Make sure you convert all your conquered lands to your religion as quickly as possible. Sometimes it helps to send religious agents ahead of your conquering armies to get a small head-start.
5. Garrisons have a lot to do with loyalty. With most provinces, one unit of 100 peasants is enough once the province has been yours for a while (some provinces, like Portugal, are more rebellious and require larger garrisons). I prefer small garrisons in most of my non-border provinces, as this keeps my upkeep costs small and enables me to keep taxes low.
6. Some buildings affect loyalty. In general, you should do at least some building-up in your conquered provinces, as this will make the people happier. Castles and religious buildings are of particular note here.
7. Certain events can cause sudden drops in loyalty. These include famines, diseases, floods, and other disasters. If a disaster occurs in one of your provinces, check its loyalty level and take appropriate action, such as lowering taxes or increasing the garrison.
8. The virtues/vices of your ruler have a significant effect on loyalty. It always helps to get the Builder virtues (especially Magnificent Builder) as quickly as possible for a new ruler, as this increases empire-wide loyalty. Often, when your ruler dies, his heir will not have the same virtues, and this will cause a loyalty drop. Whenever your ruler dies, review empire-wide loyalty and start working on building up the new ruler's virtues.
9. Under no circumstances should you allow your ruler to be isolated from the rest of the empire. For example, do not send him overseas on a crusade or to capture an enemy island. Areas of your empire that do not have a clear route to your ruler's location will suffer a sudden, catastrophic drop in loyalty, resulting in mass rebellions.
10. Place spies in your own territories to increase loyalty. Spies in enemy territories undermine loyalty there, but they can be caught quite easily.
11. At least once during a campaign, when your empire gets very large, you will suffer a large, multi-province rebellion. I think this is a built-in feature to make the game more challenging, and is virtually unavoidable. You can limit it by following the above advice, and most of your lost provinces will be easy to recapture. It should only happen once; if it happens more than that you are doing something wrong.
I hope these points help. If you do it right, you will have very few rebellions at all.
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