I agree with movie theaters. I have had several movies ruined for me (when I paid a lot of money to go see them) because some kid won't be quiet or a baby is screaming (and even then most movie theaters don't ban kids until after a certain time of night, when the kids should be in bed anyways).
Some hotels I can understand to, if it is a nicer hotel that has standards for certain things, like noise level, kids can be disruptive to other paying customers.
Even grocery stores is understandable. More than once have I been grocery shopping and kids are screaming and crying and throwing a complete fit in the aisle. I feel bad for the parent. Also I've seen kids knock over displays or pull things off shelves and just leave them on the floor, making a huge mess.
I work at a retail store that sells many collectible brands of things (kinda a bit of everything, we sell Waterford glass, Fitz and Flode dishware, Dept. 56, Amia Glass, and many other breakable things) and our store is very crowed with stuff, and people feel it is ok to bring their young kids into our store when there are so many breakable things, some that look like toys but are for display purposes only. Well behaved kids I don't mind, as we do sell some kids things like webkins, but when I've spent hours trying to arrange the shelves and tables to how my boss wants it, and a kid comes and moves everything (even adults do it too which is annoying) or breaks a $100 item (lucky for them we don't have a "you break it you buy it" policy (lucky for us employees to, especially around christmas as we always break ornaments)) or gets finger prints on all our cases. Some kids don't listen, I've had several mothers scream at their kids constantly not to touch anything, yet the kid still touches stuff.
I understand the decision to not allow young children for the sake of the merchandise or the peace of the other paying customers. Heck I wish some stores (like the one I work at) would ban teenagers who are obviously not there to buy anything (we had to kick out a group because they thought it would be fun to play hide-and-seek in out store).