A simple approach is to tally the number of pageloads for the page that contains the video, rather than the number of times the video itself is played. First, create a table in your database that contains these fields:
DateTime date // date of pageloads -- we'll get to this in a minute
int videoID // Unique Identifier for the video loaded
int count // Number of pageloads
When I tally pageloads, I do them by day so I can compile statistics over time. Of course, you can use a different granularity depending on your particular needs.
Additionally, I don't particularly like writing to the database with each pageload, so I have a class I've written that caches the hits, then writes them after every hundred hits or so.
In this class, I also retain each user's IP address. This allows me to ferret out duplicate pageloads. A subsequent task, which I'm working through in my own hitcounter, is to triage humans, legitimate spiders and unwelcome bots.