The major US cruise lines - RCCL, CCL Princess etc.. do provide a conditioning shampoo and soap (liquid) in the showers and bar soap for the sink. However, if you are picky about your shampoo, you might wish to bring your own.
Some cruise lines also provide an assortment of bathroom items - razors, lotions, toothpaste etc.. but these are give aways provided as marketing tools from the manufacturers, so the content and make up can very from cruise to cruise. You can also purchase many toiletries in the ship's store.
The best rule of thumb would be that if you have to have it, you should bring it with you.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013