Everyone has different opinions on this, as you can see, but I think there's a window where it is really not-ideal. I would be fine taking a baby up to about age two - can nap in strollers, pretty portable, will be happy in the nursery, cheaper to travel with, etc - but age 2 was not a good age for us to have our younger child on a cruise. We still had an amazing time, but if we had known what we do now, we would have waited a year. This is partly because of sibling dynamics - our kids were 2 and 4, so we had one in the nursery and one in the club, would have been better if they could be together. But also, both my kids needed their routines to be really set at age 2-3, or else they'd be volatile. So, that meant 2 hour naps every afternoon, or else meltdown central. So one parent was stuck in the stateroom with a sleeping toddler every afternoon. And MANY of the activities on the ship -- way more than I had anticipated - were for age 3+. She basically could do Nemo's reef and that was it. She LOVED Nemo's reef, and spent hours there every day, but it's not the most fun area for an adult to supervise, and there are enough unsupervised 6-7 year olds running about in there that a 2 year old really needs supervision. The toddler times were fine, but not great, and didn't offer enough gross motor play. The "wake up with Disney jr" was scary and loud for her.
(obviously there were awesome things, and the good outweighed the bad, but in retrospect, we wish we'd waited. We're going back next week at 4&6, which is going to be pretty perfect, I think).