The procedure is that you are responsible for getting to the next port for the ship where you can board. However if you do miss the ship you need to contact the cruise line to let them know you plan to join the cruise at "whatever" port. This is if you miss the ship on embarkation day.
If you miss the ship at a port-of-call during your cruise, the cruise line will have agent for each port. This agent's name and phone number will be listed on the port literature you will be given for each stop. Never leave the ship without this information.
So i understand in general it is no problem to board the ship at another port.
It *is* a problem. It's just that it is allowed although it needs to be avoided. For example, if a passenger decides to purposely miss the ship's departure from X port because they want to spend more time there, and then they plan to return to the ship in Y port. All the ship's staff knows is that the passenger never returned prior to leaving X port. This can create problems with the possibility of searches being performed for the passenger, delays and hassles for the other passengers, etc. There can also be legal issues depending on the port. Some countries have different immigration rules for cruise passengers stopping by for the day, as opposed to someone who flew to that country.
It almost sounds as if you plan on "missing" the ship. Don't do this! While they have put procedures in place to handle this when it occurs, it does not mean that it is acceptable to do it. As Dave pointed out, it can make for a huge immigration control/ customs problem in foreign ports.
As has been pointed out, missing a ship can cause a lot of inconvience to the other passengers and staff, but there are situations where it does not necessarily cause immigration problems.
For example, two ports in the same country. In Spain and in Italy (for example) you can drive(or overnight train)from one port to another. I would think that the same would be true of Greece and the Greek islands, but I have no first hand knowledge with that one.
In the Caribbean, islands are so close together, eg. Puerto Rico is about 65 miles from St. Thomas (no immigration problems) that you can fly or take a boat from one to the other. On a recent visit to Tortola (BVI) residents told us that they motor over to San Juan to shop.
I suspect the same holds true for some Alaskan ports and some east coast US ports.
So, depending upon the port in which you elect to miss a ship it can be no big deal - except of course for the inconvience factor to others. I don't know how long a ship will delay departure because of late arriving passengers, but perhaps some of our more experienced posters can answer that one.
Note: If you plan on missing the ship, don't take an overnight bag with you - that will make your "I just missed the boat" excuse a little hard to believe