Specifically, I tip our room/housekeeper staff at the beginning of the cruise (about two thirds), and then a final third at the end. Same for wait staff in the dining room. This helps ensure that we get a quiet table out of the way, where Asta the service dog won't get stepped on, and won't disturb other diners.
I do not profess to be an expert on tipping, so I refer you to this article on Cruise Critic:
Here are some of the highlights that I use as a guide (note that this assumes no tips are included in the fare):
cabin stewards $5 a night
For attentive service by butlers who have served as valets, brought trays of tea or hors d'oeuvres, and kept the liquor closet filled, $5 a night at the end of the cruise.
room service stewards $2 per visit.
I give my regular bartender $5 a day.
If I go to different bars, I leave $1 per drink with the bill -- on top of the automatic gratuity (usually 15 percent).
Maitre d's and Head Waiters
I usually do not tip the maitre d'.
On the other hand, I tip head waiters $1 for each night I am in the dining room.
If, however, the head waiter has promoted ordering off-menu items, prepared special dishes tableside or provided a cake for a special occasion, I would add an additional $5 per person, per service.
Dining Room Waiters
I tip dining room waiters $5 for each night I am in the dining room.
Baggage Handlers $20
If I am in my cabin when my bags are delivered, I give the handler $1 per bag, just as I would a bellman ashore. Likewise, if I am escorted to my cabin by a steward I'll never see again, I give him/her $2.
If the spa has added a 10 or 15 percent gratuity to my bill, I round it up (in cash) to between 18 percent and 20 percent, which is what I would normally tip at home.