The knives I personally use the most often are:
Santoku - I use this by far the most. It looks sort of like a cross between a butcher knife and a meat cleaver. The blade part of the knife has less of a curve to it, and the sides of the blades have indentations in them like a cheese knife. The wide rectangular shape of the knife is fantastic for chopping vegetables since it keeps the blade from swerving when you cut through something like a tomato or an onion, so you get nice even straight slices. You should definitely have one of these, and perhaps a spare one if you are working with raw meats and veggies.
Boning Knife - this is a thin long blade, which is flexible. Perfect for cutting around bones to remove the meat, hence it's name. This is indispensable for de-boning stuff like fresh chicken thighs or breasts as well as removing the skins and trimming off excess fats. I try not to buy already boneless skinless chicken, since I like to do it myself and save the bones and the skin for stocks. Plus I'm not limited to just boneless skinless chicken in my fridge.
Bread knife - a long serrated blade. We all need these for fresh loaves of bread. Regular blades often wont cut through bread easily and you wind up smashing the loaf or bun in the process.
An all purpose serrated knife - generally speaking I hate serrated knives, especially when cutting raw meats, as well as using them on cutting boards because they have a tendency to snag on a lot of stuff. Plus it's a total nightmare trying to chop fresh herbs with them since they don't really chop at all. But there are some instances where they work well, such as slicing through a delicate sandwich without smashing it. I listed this knife here along with the bread knife because the bread knifes aren't as fine as a serrated knife.
Optional (imo):
Meat cleaver - I mainly use this to separate chicken wings and drumettes when I am making a huge batch of buffalo wings at home. The weight of the blade, and the thickness of it help cut through and separate the joint bones easily. I don't like using my Santoku for this since it's lighter and doesn't have the weight to it, plus the blade is thinner and therefore more delicate. I also use this to break down whole chickens.
Pairing knife - personally I almost never use these, but some people can peel stuff with these at lightning fast speeds. My mom can peel potatoes super fast with these, I can't seem to get the movements right, so I stick with a peeler instead.
