Packing for an Alaska cruise takes some thinking....you'll need a few pairs of jeans or what ever pants you like to wear, sweat-shirts, t-shirts and throw in a pair of shorts or two, you could see some nice warm days. Also some rain gear, most likely you'll see some rain, after all it is a rain forest.
Then just follow the dress code for each evening for dinner, usually 2 formal nights, so bring your nice stuff :-)
Here is a link to a good article on packing for Alaska:
Packing for Alaska