My little family loves them. Mostly Royal Caribbean cruises, all 'big ship' - my wife and I did a Celebrity cruise once. There's a lot to like.
1.) Mainstream 'family' cruise lines offer a good value for a decent price in a largely all-inclusive package with a wide range of entertainments (some included, some optional extra cost) appealing to young and old, and multiple dining venues.
2.) Cruising offers people who've never left the U.S. the option to get out and visit an 'appetizer sampler' of multiple foreign destinations with the security of the big 'mother ship,' and cruise line-organized guide-led excursions covering a wide variety of entertainments and desires. You don't have to research a foreign destination like some of us do when we plan a dive trip there.
3.) It's a pretty safe experience, unless you wander off in port on your own somewhere bad.
4.) The stateroom attendants and dining room staff provide excellent service, so you can enjoy casual or fine dining and never have to worry about putting away or washing dishes, making beds, etc... I suspect many women in particular enjoy that side of things, since they're often the one doing such at home.
5.) You can buy a photo package (I prefer digital) and get quality professional photography of your family in varied settings and backgrounds, and since there's often a couple of 'formal nights,' you might even get your family to dress up and get some 'nice' pictures (normally I regard suits as 'monkey suits,' but even I appreciate some of our photos - Royal Caribbean photographers even made me look in pictures, and that's no small feat).
6.) At least some ships have nurseries, and varied level kids' clubs. Some ships have water slides and other amusements kids really enjoy.
7.) Some of the production shows in the evenings are really good, and in some cases you can exposure your kids (and yourself) to Broadway-style plays and other diverse entertainments they might not get back home.
8.) Excursions offer diverse experiences. I've interacted with dolphins and manatees, held a sloth, ridden through rain forest canopy in an aerial container, parasailed, snorkeled, even scuba dove and more in part thanks to cruising.
9.) The ship itself is often comfortable, beautiful and has diverse (and often very weird) artwork scattered throughout.
10.) Don't underestimate the 'appetizer sampler' view of the varied ports. St. Thomas is mountainous but seems a bit dry, Curacao and Aruba are arid, St. Lucia is mountainous and very lush, you can get a first hand look at the topside without having to commit to a dedicated trip to that destination.
Cruising wouldn't be my choice for a solo dive trip, but for a family trip to enjoy and provide our kid enriching experiences in a conveniently packaged, easy to plan and execute form that's decently priced, it rocks.
Note: We're mainstream 'family cruise line' people who cruise Royal Caribbean big ships (Voyager, Freedom and Oasis-classes). Carnival and NCL would be similar from what I understand (as would Celebrity and Princess, though less kid-focused). Kiss 'budget-friendly' goodbye if you go with a Disney Cruise, and the 'luxury lines' (e.g.: Cunard, Silver Sea) I don't follow.