It is perhaps the chef's most valued tool and even when cooking at home, a decent one is an absolute must!
I share the same opinion of most chef's that there are three core knives that it's worth spending a bit of money on. A blunt cheap knife will cause more cuts and also invariably need replacing more often so it's worth the investment.
The three knives that I believe to be essential are the following:
8" Chef Knife.
This is your "go-to" knife for pretty much anything you need to chop or slice. You can use it for purposes it shouldn't technically be used for (you can even slice bread with it at a push as long as it's sharp enough), and it will become part of your hand when preparing anything! I couldn't live without mine. 6-8" long and about 1 and a half-2" tall is an absolute minimum though for safe chopping... trying to cut through butternut squash or turnips with a vegetable knife is going to lead to a really long and painstaking process at best and missing fingers at worst! You should also make sure that the blade is rigid and not flexible, you should not be able to bend your chef's knife at all.
3-4" Vegetable, Utility or Paring Knife.
When you need to get up close and personal to what you're preparing or if the peeler has gone walkies, absolutely essential! You'll find that you can often use this knife in place of similarly sized knives like filleting knives, just make sure that you wash it as thoroughly as you can (like all kitchen equipment) between different applications. Like I said above, make sure the blade is rigid!
You can use other knives to slice bread but it isn't easy... I find it incredibly difficult even with the sharpest blade to get nice thin slices. If you buy sliced pre-packaged bread all the time and don't need to buy a bread knife... erm... well.... nuff said.
Those are the essential ones but there are other knives you may wish to consider:
10" Ham/Salmon knife.
Thin blade and perfect for slicing smoked salmon or cooked meats like a joint of ham (duh!). Also a good knife to use when cutting delicate things like soft cheeses, pate and terrine.
So you've rolled your pastry and cut it out into shapes.... how ARE you going to get it off the work surface without butchering it with a fish-slice or ruining the shape with your fingers??? Mr Pallet Knife will prevent fingers from getting over involved. Pallet knives come in handy all over the place so it's worth buying one and the great thing about them is that they need not be expensive or sharp. Find one that's got a broad, thin blade and you're laughing.