We cruised with DS when he was a toddler, and will be going again this year when he's 3.
For us, we will take a vacation every year, as a family. It's just a question of where. So we evaluate the relative merits of visiting family, staying in a land-based resort, and cruising. When it's land-based resort vs. cruising, for us there are lots of benefits to cruising with little ones.
1. You're always very close to your room. Ideal for cranky LOs who need naps. Ideal for quick clean-ups.
2. No down time while you transition from one activity to another. You don't have to drive anywhere, and can very quickly go from having a snack to taking a walk to checking out the theater. Easier to deal with short attention spans.
3. Always tons of stuff to do a walk or elevator ride away. Walking the track, playing mini golf, relaxing at the pool, and there are tons of activities on the ships each day.
4. Beach outings are great with toddlers. Pick your beach well (and bring rash guard suits for the little ones), and babies will happily play in the sand, walk in the water.
5. Stateroom attendants on a ship are far more attuned to your needs than housekeeping in a land-based resort. So you can quickly get them up to speed on when nap times are (so don't be in the room cleaning then). Trust me, it is extremely annoying to come back to the room to find housekeeping in it and they won't leave.
What we did with DS was play in splash pool with him (we sailed RCCL Freedom of the Seas, there was a spray area like Nemo's Reef). Walked around the ship (sometimes in his stroller, and he'd fall asleep). Played mini golf. Went to the theater, but did not expect to see a complete show. Beach days when in port. RCCL had family play times in some of the kids spaces, with toys provided, and it is my understanding that
DCL has similar open house hours you can bring the little ones to and play with them. Character interactions (RCCL had the Shrek characters).
We would only cruise with little ones in a balcony. We needed someplace to be while DS was sleeping, since his bedtime was well before ours. Mostly we stayed out there and talked. One of us would run to get snacks or drinks. Sometimes I'd shop and DH would stay on the balcony, or I'd read out there and he'd gamble.
No, it's not like cruising when you're just a couple. But it was inconceivable to us to vacation without our son, so it's really just a question of which vacation would best suit our needs, and we thought the cruise was a good fit.