Flat or Matte; no shine is what you get here. Joanne Day with the Daystudio said "If you paint a dining room a dark colour and you leave it flat, at night it will look black", better to give it a sheen and then (if you have recessed lighting) the wall will reflect the light back into the room".
The problem with using flat paint in the past, was that it wasn't washable, (until paint companies came out with washable flats). And the plus side is that you can touch up flat paint where you cannot with any other sheen. If you do, you get flashing, which is a phenomenon where the additional coat or sheen builds upon the first–which is why you have to re-paint the space when your tenant moves out.
Flat paint is also good for walls where you want to cover a lot of imperfections as it doesn't reflect light.
Eggshell; the low sheen of the shell of an egg is what this looks like on the walls. It's the sheen I specify the most. Good for any room in the house (including the powder room) except really high traffic areas where a shinier finish would be even better. This room below, both the ceiling and the walls are painted in an eggshell finish.
Pearl; These days where latex paint is much preferred to the toxicity of oil, at least use a minimum of a pearl finish if you are painting trim, as latex does not take the beating oil will take which is why furniture and trim are usually painted in oil.
Satin; It's the one I specify the most for trim (in oil, with Benjamin Moore you can't get latex in a satin finish anyway) because it's self-leveling and has a smooth, velvety look to it. However, with latex paint becoming more and more durable, you can now paint trim in much lower sheens with Benjamin Moore's new Aura which is great on trim (and you can even do a flat in a bathroom).
Semi-gloss; This finish has a slightly glossy appearance but is not wet looking. Good for high-traffic and high-moisture areas like laundry rooms. Keep in mind that the imperfections in the walls will reflect in the light with this finish.
High-Gloss; The trim in this hallway [below] is definitely high-gloss. The more formal your decor is, the shinier everything gets (and it's the most durable).
If you pick the same colour for the trim as the walls and you change the sheen, many times it can look like a completely different colour, or at the very least, look like you tried to match it and failed, so make sure you test it before you start painting it all. This happens many times in a contemporary space where the woodwork is painted the same colour as the walls (but in a different finish)!
One more very important point; what one paint company calls eggshell, another may call semi-gloss, so if you don't have a lot of experience specifying a certain brand of paint, make sure you pick up some sheen samples which every paint store will supply.
Living Room ~ Matte or Eggshell
Family Room ~ Matte or Eggshell
Kitchen ~ Pearl
Bathroom ~ Pearl
Powder Room ~ Matte or Eggshell
Bedroom ~ Eggshell or Matte
Kid's Bedroom ~ Eggshell or Pearl
Foyer ~ Eggshell or Washable Flat
Staircase Walls ~ Eggshell or Washable Flat
Hallways ~ Eggshell or Washable Flat
Trim and Doors ~ Satin or Semi-Gloss
Stucco – Matte or Eggshell
Siding – Eggshell (to repel dirt)
Trim & Doors – Semi-gloss (for durability)