Very nice attention to detail (Oct 2014, Western Caribbean)

My first cruising experiences were with Disney, so I've had high standards from the beginning.  The RCL Navigator was very close to Disney in quality, and head-and-shoulders above the Carnival Triumph- and Magic-class boats.  (Life is too short to cruise Carnival... no matter how cheap.)  I haven't been on the Norwegian lines in a while, so don't remember well enough to compare, but I think they're comparable.  I've heard too many people say Princess is like Carnival, so I haven't even tried.

Pros:
Attentive dining room and cabin staff.  Outstanding entertainment (especially the ice show). 
Excellent quality food, both in the main dining room and WIndjammer.  The 24-hour Cafe' had sandwiches to die for - and I don't generally get excited about sandwiches.  Try the Jive Turkey and muffuletta.  They're served dry, so find the condiment packages. 
Morning room service was always prompt, even on port days.  The fruit plate was wonderful!
The Windjammer is entirely indoors, making it much eaisier to find a seat in hot or inclement weather. The WJ staff constantly brings you water, iced tea, and a yummy strawberry-kiwi water.
Lobster night is spectacular.  Someone at my table ordered two entrees, and ran out of time to order a third. 
Good general layout of the ship; it's easy to get wherever you're going, except Johnny Rockets, which is accessed from outside.
Really nice, quality ship mates; dinner was always interesting and we made some lasting friends. 

Cons:
The dinner seating only serves 3 courses, so if you're accustomed to 4, you'll need to double-order an appetizer.  There were one or two appetizers I didn't care for (e.g. chilled fruit soups), so I was glad to leave one untouched.  
Elevators: There were fewer elevators than on most ships, but they were generally larger.  Still, on formal nights, when women were reluctant to climb stairs in ultra-high heels, the wait for an elevator was rough. DItto for getting on and off the ship.  Be prepared to climb stairs - a lot.

Ports of call
Roatan, Honduras.  Docked port-side (but nothing to see but a bunch of trees).  The Roatan stop was almost a waste of time.  Maybe 5 shops are open at the pier with overpriced, unoriginal merchandise.  No internet, but I did find a tiny booth with $1/min calls to the US.  Tours will take you past grinding poverty (tough for sensitive children).  By all means, stay within the touristy pier area, where you're protected from aggressive begging.  It's a good day to stay on the boat and chill, or take classes (belly dancing and ballroom were great).
Belize City, Belize - ships tender about 5 miles out - plan 30 minutes to get to/from shore.  The bar right by the pier (second floor) offers free internet service; just buy a $2 can of soft drink.  It's also a great place to watch the line for the tenders, and choose your time to get in line.  The best prices on prescription pharmaceuticals was in Belize.  Cozumel was twice the price.  
The shopping at Cozumel was excellent.  Internet service was easy to find in local bars.  There were 4 mega ships that day: the RCL Allure, the RCL Navigator, Carnival Magic and Dream.  Tourists vastly outnumbered the locals.  It was a little crowded, but not as bad as I thought it would be. 

Suggestions:
Events, like giving out ice show tickets, start the very first day - even before the ship departs - so find a Compass and get going!
With such outstanding service, the staff deserves higher tips (so budget for it). 
The really good food in the Windjammer is at the very back (onion gravy over mashed potatoes - yummm!).  There can be lines at peak times.
People dress well for every evening meal.  Formal night often means a tux, but almost always a suit. Ladies often change into nicer dresses for dinner (no flip flops, even if they're formal).
Galveston on/off ship:  Boarding is from boarding from 11:30 - 3:00.  (We asked; the staff at terminal said best time to arrive was either 9:30 or after 2:00.)  We arrived at 2 pm and sailed right through, with a brief wait to get our room cards.  leaving the ship, we were in the first self-assist group (pick up a ticket at Customer Service the day before, being queuing at least 15 minutes early) and again, sailed right through.  Both were between 30-45 minutes.  The Galveston terminal is largely un-air conditioned, with almost no seating, and waiting in line can be miserable.  
Bring an ice chest, and stop by the local fish market (the pier is just down from the cruise terminal) to buy some fresh shrimp and fish.  They'll supply the ice.  Ask any local for help.