Cover the pot if you want to keep liquid inside; leave it uncovered if you want liquid to evaporate. A lid traps steam, raising the temperature faster, helping food cook sooner, and preventing liquid loss. An uncovered pot lets steam escape; the sauce thickens and the flavor concentrates, but cooking takes longer. So the answer depends not on the name of the dish but on what you want to do with the liquid at that point. You may change the approach several times during the same dish.
When the lid is on, a small steam chamber forms inside the pot. Because steam transfers heat much more effectively than air, the top of the food heats as quickly as the bottom and the cooking time is shorter. Almost no liquid is lost because rising steam condenses under the lid and drips back into the pot. This is why rice pilaf, dried beans, stuffed vegetables, steamed dishes, and other foods cooked slowly over low heat are cooked covered. A lid also retains heat: the same dish uses noticeably less heat in a covered pot. It is important for the lid to fit the pot properly; a loose-fitting lid lets half the steam escape and reduces the benefit of cooking covered.
With the lid off, steam escapes freely and liquid evaporates. This is the most natural way to thicken sauces: simmer sauces uncovered when you want them to thicken without adding starch or flour. For the same reason, tomato sauce, stock, and syrup are cooked uncovered. An uncovered pot also keeps the temperature inside somewhat lower. That is why foods most likely to boil over—milk, pasta water, and foaming legumes—should be cooked with the lid off or at least partly open. Since water evaporates quickly during uncovered cooking, check the food more often; a sauce left unattended for ten minutes can stick to the bottom of the pot.
Most dishes actually call for both approaches in sequence. A common order is to cook the food with the lid on over low heat until the ingredients soften, then remove the lid and simmer uncovered for a few minutes until excess water evaporates. This shortens the overall cooking time and thickens the sauce. The reverse can also be useful: if a dish loses too much liquid early, add hot water and cover it. Leaving the lid partly open is a middle ground and the most useful setting for maintaining a gentle simmer.
There are a few cautions. Do not cover food while frying or sautéing; steam trapped under the lid wets the surface, so the food steams instead of browning. When lifting the lid, tilt it so it opens away from your face, because steam trapped underneath can cause a more severe burn than boiling water. Condensation on a glass lid is also informative: when the fog disappears and the food inside becomes visible, it indicates that the liquid has decreased. When rice is resting after cooking, do not lift the lid; each time you open it, steam escapes.