We just returned from back-to-back cruises on the Jewel of the Seas. On the first (7-night) cruise we had two formal nights. There were a surprising number of men in tuxedos, and it seemed most of the rest were in suits. On the second (14-night) cruise it seemed to me that a LOT of men had on a tux - a higher percentage than on the previous cruise.
Personally, I don't mind dressing up for formal nights (although 3 formal nights in 14 days is a bit much). I always bring my tuxedo. To me it's just a suit with a thing around my waist to keep my stomach in.....
I have no problem with guys who don't wear a suit or tux to the dining room, but it really frosts me when I see someone coming in to the dining room in jeans, wearing a baseball cap.
As long as Royal Caribbean has a "suggested" dress code, you will see everything.