First of all, let me say that this is not an all inclusive list. Each Tiger will more than likely get a list from your sailor's ship. 

I highly recommend that you take the time to read through Admin Paul's blogs about his Tiger Cruise in 2009 on the USS Theodore Roosevlet. It does give you some real insight as to what you might expect while on board.

Keep one thing in mind, you are being allowed to sail on a United States War Ship. Not the Good Ship Lollypop. They will accommodate your needs as much as possible, but the sailors on board are still hard at work protecting our freedom. 

Okay, here is a list of recommended items you need to take:

Get a duffel bag. Hard case luggage is going to be very difficult to store.

Shower soap and a seal-able cup to put it in.

Towel

Wash cloth

Shower sandals. (You will be walking from your berthing area to the shower and head)

Robe. I suggest a heavy one.

Razor (Optional)

Small flashlight.

On the whole, Tiger Cruises are three days. Some may go longer, some shorter. Pack enough clean clothes. You will not have access to any laundry. They also keep the air conditioning cranked up pretty good below decks and in the berthing areas. You might have room in your duffel for an extra blanket.

Two pad locks. You will want to secure your valuables in your rack, and you may also get the use of a locker.

Camera. I suggest one with rechargeable batteries. Charger

Cell phone and charger. (iPad?) Mostly for taking pictures and video. Keep these items under lock and key when your not using them. There are power outlets in your rack.

If you wear a ball cap, it may not be worn on the flight deck if you're going on a carrier. They don't want it blown off your head to only get sucked into a jet engine. (Trust me, you can not afford to replace an engine on an F/A 18 Hornet.)

Depending on the time of year it is, and the weather, and geography, you will want a jacket to wear on deck. Doesn't matter if it's a carrier or a destroyer, it can get pretty cold when those 40 to 50 knot winds start whipping around you. 

If any of you veteran Tigers have anything to add to this, please let me know so I can add it here.