It depends. Sometimes I have dreams that appear to chain throughout the night but are different enough in terms of what happens that if feels right to separate them into their own little thing. Often there's a break in between them that is psychologically perceptible even if nothing has stopped the dream, I just don't know. This gap may be the result of stress, poor memory in remembering the dream or difficulty in staying aware as it is going, so I witness chunks of something and miss more of it when I wake up. Naturally the more "vivid" a dream the longer I can focus on the story and more likely I'll end up labeling the event as one long dream. If a story is short and simple then a dream is anything that happens before I woke up.

Since stress plays a huge role in the amount of dreams I can remember, I'd say I average around 2-3 dreams a night. Recall crashes once I'm stressed and luckily I'll have it in me to remember the shortest of dreams, if anything.