BAD GAS

If your mower doesn't want to start in the spring, the first thing is to suspect that the gas has gone bad.
That may sound odd, but trust me, the half-life of gasoline is only a couple of months.
One way to test is to splash just a tiny amount of gas into the carb (if you can reach it) and see if it pops.  Some of the spray carb cleaners are very flammable, and will do the job too.
You need to drain all the gas and replace it.  On many mowers there is still gas in the bowl (even B&S mowers with the carb on top of the tank may have a bowl built into the top of the gas tank) which will need to be drained before things start working again.

Next time drain the tank and run the engine until the bowl is empty, or use a gas preservative like Sta-Bil before you put the mower away for the winter.

More and more, I'm seeing water in the gas.  This can happen even to mowers that have been stored out of the weather.

Sometimes, it's the GAS CAN that's been stored outside.  

Even if they don't get wet, the tank or can can breath in humid air, then have it condense out when things warm up or the engine gets hot.

Gas floats on water, so the water goes to the carb.