As a hobbyist knifemaker who does a lot of kitchen knives, this is something that I think about quite a bit. People will obviously answer this question very differently based on their experience, skill, preferences, what they cook, and what they are most comfortable with. I have been making and using a lot of different knives over the past few years to work out what I need and what I like. I can do basically everything I need to do with just a few knives.
Here are the most important knives for me:
1) a primary chef's knife. I favor a 9" gyuto, but I have been using a 7" one for the last year and it is only rarely not enough.
2) a serrated bread knife. Mine is 8", but I want a 10"er. Some people advocate using this to slice meat - I am much more likely to use a gyuto for this than I am a serrated bread knife. There are also people who use a straight-edged slicing knife or a chef's knife for cutting bread. I strongly prefer serrated, particularly when I'm cutting something with seeds or a hard crust.
3) a 3" paring knife. I find that any longer than this is unwieldy for what I use it for, and smaller is not big enough for what I use it for.
I can do basically everything with these three knives, but there are some things that I do that other knives are better for. Here is my second tier:
4) a gyuto can be used as a slicing knife in a pinch, but a 10-12" sujihiki is better.
5) My gyutos have very fine edges. As such, they are better-suited to cutting things that don't offer resistance. For the rest, I like a knife that can handle rougher tasks, like a ryodeba or a honesuki.
6) a 6-7" petty. Not necessary, but there are certain tasks that they are great to have for.
7) a 6-7" nakiri. A 9" gyuto can do just about anything. But sometimes a smaller, more delicate knife is better.
I don't butcher anything, so I don't need any butcher knives. I us a petty or a paring knife as a boning knife in the rare times when I want one. I have more knives than this that I use occasionally, but this list represents what I need and want most.
And because this thread could use some knife porn, here is a set that I made a couple of years ago for my then girlfriend:
Everything she thought she would need: a 9.5" sujihiki, 7" gyuto, 5" deba, 5" petty.
- Chris
ETA: I should also mention my feelings about stainless and carbon. I like carbon steel a lot, but I think that there are some knives that are better in stainless. My rule of thumb is that if the maintenance for a knife in carbon steel takes longer than I usually spend using the knife, I prefer stainless. If all I have to do is cut a lime in half, I want to be able to put the knife down dirty and finish what I'm doing before I wash the knife.