Why won't my mercury 40 hp outboard motor fire?

One possible reason is that the carburetor is gummed up. This will happen if you allow fuel to sit in the carb for extended periods without running it like over winter. You should always disconnect your fuel line while the engine is running and let the gas in the carb run out if it is going to be idle for awhile. That is what my problem was and once I figured that out it has started on first bump of the ignitioin even after sitting idle for several weeks. Outside of that it of course could be the plugs, water in the gas, or more serious matters but those are less likely. Try a carb cleaner or engine start spray into the intake to get it going but most likely you will have to have the carb removed and cleaned or rebuilt.