Usually yes but if it states "Cruise Only" then the answer is NO. You don't say who you are considering going with but regardless of that you should check the details of each cruise. If it gives information about various departure airports and flight supplements then it is likely that flights are included. Lines such as P&O do include the cost. I recommend you make any enquires and booking to your travel agent by phone (or visit personally) to ensure that you know exactly what you are paying for.
If it says "fly cruise", then cost of the flights is included, if it says "cruise only" then flights are excluded. If your flights are booked with cruise line as a package then any delays or problems are down to them. If you book your flights independently, then any delays are down to you.