I would say Space Mountain has zero big drops. It does have a couple of minor hills but nothing in comparison with a true roller coaster hill drop. Having said that, it still is a great ride.
There are members of my family who will never do roller coasters. Don't like the stomach in their throat feeling. Even somewhat hesitant about Splash Mountain. But they love Space Mountain. It is more turns than drops and hte drops are not like roller coasters where you climb, climb, climb and then go over and down. Much shorter quick drops.
To be clear for any new people reading this thread: there are no upside down loops on Space Mountain. The only WDW attraction that goes upside down is Rock 'n' Roller Coaster. Of course, during or after riding the Teacups, some people have been known to turn upside down and return their breakfast to Mother Nature, but that's an entirely different thing.
There aren't any big drops, but I did read that after it re-opens (tomorrow, I think) the ride itself will be much darker so everything is more of a surprise.
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