I, fortunately, have never been sick at a Hilton brand property... other then a small cold once or twice.

The last time I was sick was when I was 12 or 13, in some Mom and Pop motel in Hershey, PA with immediate and some extended family.
I got the stomach flu and it hit me in the middle of the night. Since I was in a strange place I got out on the wrong side of the bed, realized I had gotten out on the wrong side and tried to make my way back the other way towards the bathroom. Too late... my choices were puke on my grandfather who was sleeping on the floor at the foot of the bed or puke on the bed. I puked on the bed.
Fortunately the blanket and the comforter were not hit, just the fitted sheet. We flipped the mattress and all was good, except for me. I spent most of the night sleep sitting by the bathroom.

Not a very fun vacation, as whenever I would get my will up to go on a ride I would take a look at it and feel queasy.
I ended up only going on two rides at the park. The Bumper Cars and the "How Hershey's Chocolate is made" ride.

Although now that the kids are along I am sure we can expect to have many fond "being sick" memories in Hilton properties around the world.