We often try to be on as early as possible. Most ports begin boarding between 11am and 12pm because they have to get everyone off the ship from the previous cruise and clean up the public areas that were being used as the previous passengers waited to get off. But, once the boarding begins, the cruise has officially started. The buffet is open as are most of the bars, while the band plays poolside. I've often been pleasantly buzzed even before the muster drill, but that's all part of the fun of cruising. The shops and casino won't open until the ship is in international waters though.
Your cabins are usually not available until after 2pm and the luggage comes after that. So, make sure to carry on anything you'll need like medications and such.
If you can be at the terminal early, you'll get on early. But, if you can't be there very early, I'd wait until after 1pm to avoid long line and uncomfortable waits. Since we'll be cruising from our home city again, we're going to try the later boarding at 1:30 to see how much shorter the boarding process is.
1999-RCCL Viking Serenade-Baja Mexico
2001-Carnival Ecstasy-Baja Mexico
2002-Carnival Ecstasy-Baja Mexico
2003-RCCL Soverieign of the Seas-Bahamas
2004-RCCL Legend of the Seas-Mexican Riviera
2005-Carnival Paradise-Baja Mexico
2007-Carnival Elation-Baja Mexico
2009-Carnival Spirit-Mexican Riviera South
2010-Carnival Paradise-Baja Mexico
2012-Carnival Splendor-Mexican Riviera
2013-Carnival Miracle-Alaskan Inside Passage