It really depends on their position onboard. Most of the officers and upper entertainment and CD staff have e-mail addresses but for obvious reason they are not often given out. The volume of e-mail would be overwhelming if they did. Family and close friends are usually the recepient of these addresses. Now you CAn develope some very good friendships with many crewmen/women if you are willing to be yourself. My wife and I have made some lifelong friends with a number of employees, some of whom are as close as family now, and we are in frequent contact with them.
Yes, I agree, you can make some lifelong friends with the crew.....Or how about a lifelong partner! My husband was my waiter on my very first cruise! As far as their e-mail addresses, some of the newer ships, like the Voyager of the Seas, for instance, have extensive internet cafes for the crew. Others have none. You'd just have to ask the crew member with whom you're interested in corresponding.