This is from Celebrity's official alcohol policy on their website:
"Guests are not allowed to bring beer or hard liquor onboard for consumption or any other use. Guests wishing to bring personal wine onboard with them at the beginning of the cruise may do so, limited to two (2) bottles per stateroom, but when consumed in any shipboard restaurant, bar, or dining venue, each bottle shall be subject to a corkage fee of $25.00. Alcoholic beverages that are purchased in ports of calls or from the onboard shops will be stored by the ship and delivered to guest's staterooms on the last day of the sailing.
Security may inspect containers (water bottles, soda bottles, mouthwash, luggage etc.) and will dispose of containers holding alcohol. Celebrity Cruises’ Guest Conduct Policy may be enforced, up to and including disembarkation, if a guest violates any alcohol policy. Guests under the age of twentyone (21) will not have alcohol returned to them.
Guests who violate any alcohol policies, (over consume, provide alcohol to people under age twentyone (21), demonstrate irresponsible behavior, or attempt to conceal alcoholic items at security and or luggage check points or any other time), may be disembarked or not allowed to board, at their own expense, in accordance with our Guest Conduct Policy."
That said - many people do try to sneak alcohol aboard. There are many threads here in these forums on the subject and the internet at large.