How important is it to run your generator at, or near FULL capacity?  For instance, I run my Champion 4000 (max) watt generator every month or so, and I use a 1500 watt space heater set to cycle off and on... Should I be running 2 heaters (and other items) to approach the Champion's rated output, or is it ok to just keep on cycling it at about half the rated output?

I've never bothered to exercise them with more than a space heater or to myself.

I typically run around 50%. If it runs and generates a decent amount of power, you're in good shape.

Not very.

50 percent of rated load is plenty to give it a good workout.

not diesel. don't worry about it

All I use is an old 100 watt light bulb on all my gens when I exercise them.

If it is a gasoline engine, you don't need to work it hard.  As a matter of fact, you don't need to apply a load at all if all you want to do is be sure the engine fires up and runs smoothly.  Having said that, I always apply a load to each arm (120 volts) of the 240 volts.  I use a dead load which draws 900 watts (a coffee pot).  I also meter the generator output for voltage and frequency (Hz) with a Kill-a-watt meter ($19 @ Amazon).  I meter the output with and without a load to be sure that the generator puts out reasonably usable power.

I live in SE Florida so my 12 year old generator (used it in Hurricane Wilma - 2005) just finished a 38 continuous hour workout.  It ran perfectly and did its job faithfully.  Did metering during the outage and the old girl still has what it takes...  Output voltage was 120 ± 3 volts and output frequency was 60.5 ± 1 Hz depending on load.