I'm a big believer in going to your embarkation port the day before, especially if you need to fly there. There's nothing like extra time to relieve the anxiety of departure-day possibilities. If there are any type of airline or traffic delays, mechanical problems, weather issues, etc., you may not make it onto the cruise ship to spend that money you saved on a hotel.
If you get there the day before, even the night before, then on embarkation day you can wake up at your leisure, relaxed and not worried about getting to the ship. Even if you have a relaxing morning before making your way to the cruise terminal, it's worth it. Some folks like taking tours or doing some sightseeing before getting on the ship, and that's certainly possible. Getting there the day before makes the start of your vacation much more relaxed and happy.