In astrology, Sun is "karaka" of a person, his/her soul, your overall entity and being. Sun also represents father. Why? Because everything in the Solar system is derived from the Sun - remember Big Bang theory? All the planets are in fact sons of our Sun, so always worship the Sun first, everyone else later. Sun is not only the ONLY source of energy that we have, but creates and sustains all life as we know it.
Conversely, though Moon is born of the Earth (due to an asteroid impact, so the theory goes) it is Karaka of the mind, mother and your inner self. It represents your passions, desires, etc...if you got any. So dude, if there was no Moon, you'd become a mind-less person, the most obvious and important effect!! plus you'd no longer worry about anything, as you'd never mind it anyways. No matter what, never mind, right... ?!

See, I'm slowly but surely becoming an subject 'matter' expert in astrology...
Practically speaking, tides would cease to form, menstrual cycles of females would stop (no more reproduction), there'd be no mood swings, just constant good, bad, or horrible mood...!! and all the crazies in Washington DC would suddenly be alright...
Sorry but I just couldn't resist responding...

I too have thought what would happen if Mars and Saturn were (made) to disappear , how would our lives change...?! Sigh...