If I understand your post correctly, your main breaker (at the top of the breaker panel) is 60 A, and downstream from that there are 40 A fuses (i.e. breaking the 60 A breaker means that no electricity flows through the fuses). The specifics of the following pertain mostly to Canada (and for the most part, the US), but the generalities are used throughout the western world.
You don't mention what feeds this panel (is this the primary one for the house?) I hope it's not being fed by 12 gauge cable, since that's a violation of at least the Canadian Electrical Code and probably the National Electrical Code as well (the NEC is used in the US). The recommendation (at least in the CEC, which is what I'm familiar with) is that you use 12 gauge wiring for 20 A max. If you put more current than this through this cable (and the cable is buried in insulation, or in still air, or otherwise can't dissipate heat), there's the possibility that the insulation or conductor itself could get hot and/or melt and/or start a fire!
I don't know how things are wired up at your fuse panel. Are most of the loads you mentioned on separate circuits (i.e. lights on one, AC on another, etc.) that are tied together only at the fuse panel, or are these just in two really big chains controlled by the 40A fuses?
If it's the first case (you can tell because there'll be lots of wiring coming from your panel), you can (depending on jurisdiction, check with your local electrical inspector, if applicable--some places require the electrician to do this, in part or in whole) replace your fuse box with a breaker panel with appropriately sized 15 or 20 A breakers on each of your circuits. Hopefully, wiring for things like your stove or dryer (assuming you have these) are sized appropriately: if they are, you just need to find the right breaker ampacity.
If it's the second situation (you can tell because there'll only be two cables coming from your panel, along with whatever feeds the panel), in order to become compliant, you'd have to rip open walls to replace wiring (along with your panel). In many jurisdictions (again, you need to check), although your house may violate current electrical code, it may still be grandfathered in (as long as it was compliant at the time of installation / rework and re-inspection) and thus acceptable. However, unless this is a really, really old house, I don't know of too many legitimate electricians that would do anything like this, and a homeowner somewhere in the past probably did this work without consulting the code book, pulling permits, or getting an inspection.
EDIT: You might think that you're okay, for the loads you've listed (after all, they each draw very little current--except for the AC: I'm not aware of too many that are 0.5 W; 0.5kW maybe--and my intuition thinks that'd be sort of anemic), but the danger is when things aren't working properly, and you have a short, or rats gnaw through the wiring, or any other number of non-normal situations that fuse panels and breakers are meant to protect against.
