The number of ships in port on any given day can have a significant impact on your cruise experience. The more ships in port, the heavier the crowds and the greater the demand for popular attractions. The number of ships can affect everything from available taxis to seating at popular restaurants. A super-mega ship like Royal Caribbean's Oasis of the Seas carries 5,400 passengers alone, and if it is joined in port by two or three other modestly size ships, that number can double or even triple in size. Combine that with the number of locals and land tourists, and you can expect large crowds and exceedingly long waits for the most sought-after sights that you and every other tourist want to see.
While I don't choose a cruise based on the number of ships in port, I do like to check sites such as www.cruisetimetables.com or www.cruisereport.com - or, better yet, the individual port websites themselves - to find out what I can expect in terms of port congestion and how far ahead I should book an independent tour or otherwise arrange my day. For example, I might choose an off-the-beaten-track tour if I know there will be an overly large number of people in town.
Simply look up your port and the date on which you ship will be docked there, and you will learn how many ships will be docked and their arrival and departure times - especially useful if your ship is first to arrive and you want to get a head start to beat the crowds. Knowing in advance how many people will be competing for tours can be a deciding factor in how you plan your day in port.