There is no straight answer to this question, it's both a yes and a no.
Most modern cruise ships have been designed to facilitate passengers of all physicals abilities, and have wider doors and level access ways to allow easy movement of wheelchairs and flatter surfaces for passengers on sticks or crutches. Older ships will have more limited facilties and sometimes small steps between compartments. With wheelchair access becoming more of an issue, many older ships have installed small adaptions to make movement easier, such as small ramps to overcome steps, however, many of these are steeper and harder to negotiate than a purpose built access way.
In addition to the ships access and doorways, newer ships will also have more cabins designated as wheelchair friendly, with adapted bathrooms and easy to use doors and wider spaces for wheelchairs. Even on the larger ships these are still relatively low in numbers, and even on a cruise ship of 1500 cabins, there may only be 15 cabins like these.
Cruise ships are more than happy to welcome passengers of all abilities aboard and staff will readily offer assistance if there is a problem, however, passengers must be fully aware that it is a requirement that they can either be self propelled or accompanied by a family member, friend or companion who will be assisting them. Staff are not available to be move passengers around. This sounds like a strange point to mention, but there have been many occaisons when officers have been called portside to meet passengers with no ability to move and with no able bodied helpers. In these cases, boarding of the ship would be refused.
Wheelchair users and people with walking issues will always be assisted in places such as the restuarants by the waiters and bar staff, if they so wish, and often waitresses will locate easy to sit places in the bars and lounges.
When booking a cruise, it is always worth asking about the access ways and how many lifts are on the ship, it may suit your needs more to request a cabin close to the restuarant and entertainment decks to reduce the need to travel up and down decks.
Another point to consider when looking at booking a cruise is the destinations you plan to visit. Many popular ports have full and easy to use port facilities, however, the smaller ports or small island ports of call are tender ports, where the ship will anchor offshore and passengers leave the ship by either local tender boats or most commonly by using the ships own lifeboats.
This process involves travelling to the lower decks of the ship and transferring to a small boat moored alongside. This process can be tricky whatever your ability, so this could be a factor in what cruises you may wish to book.
Finally, always take a look at the organised tours available from the cruise company. These are often marked with some form of indictation as to how hard it is to undertake.
Whatever your ability, there are crusies that will suit you and your needs, to destinations you would love to visit.