Demented

In my opinion, the minimum knives needed;

Chef's
Bread
Paring
Utility
Carving
Slicing
Boning
Butcher
Fillet

A Utility knife is the best tool for task like slicing mushrooms, garlic, radishes or shallots for a salad when only a little is needed, and cutting tomato for a sandwich or a sandwich for that matter, when a paring knife is to small and a chef's knife to large.

If you roast large cuts of meat or turkeys, a carving knife will do a much better job than a chef's knife when it's time to get the meat to the platter.

For getting really thin cuts of roast meat for sandwiches a slicing knife is hard to beat.

The last 3 are task oriented knives that may not get allot of use (depending on how you prep/shop), if you buy whole poultry, fish, primal cuts of beef or pork, rabbits etc. they are hard to get by without.

Having a thinner blade than Chef's knives, Butcher knives are a good choice when breaking down meat that's headed for the grinder or the stew pot.

Specialty cutlery that gets a lot of use in my kitchen,

Cheese knife
Poultry shears
Kitchen shears
Salmon/Ham knife
Oyster knife

Lets not forget a carving fork and honing steel. While the steel will not sharpen your knives, it will straighten the edge and prolong the time between sharpening.