I have about 20 phone numbers in speed dial, over 200 Facebook "friends", almost 300 Twitter followers, over 600 LinkedIn Connections, and over 2000 people in my address book, but I know of many others. The deaths of Ernest Borgnine and other celebrities and politicians reminds that I know of a lot more people than I know, as I would be truly sad if people I actually knew died as frequently as celebrities.
I really don't know how many people I know, or know of.
We can estimate though.
Unscientifically, I seem to recognize about 3 celebrity deaths a week (including politicians, athletes, academics, and others I have heard of). (You can check this for yourself at wikipedia's Deaths_in_2012 [It might be closer to 2, in which case you can adjust the numbers accordingly]) If we assume this is steady state (I am sure it isn't), that is 52*3=156 deaths a year, or over the course of my 100 year life (I am an optimist), 15,600 deaths in my lifetime. This implies I know of at least 15,600 living people (ignoring leap years). The number of people I will know of when I am 100, avoiding senility, surely exceeds the number I know of at birth, so there are lots of nonlinearities to go around.
Of course I know more, because some celebrities will outlast me, assume half, so we add about 7,800 living people whom I will predecease.
There are many people whom I know of who died before me. Historical celebrities, politicians, etc. whose name I recognize. How many? If we assume all historic personages are in wikipedia (they are not, and certainly not all by year of death), I could go through that and make an estimate [See Deaths by year]. Of course it increases as we get nearer in time to the present (I know of a lot more people who died in 1966 than 66 AD, both because records are better in the present, and because there are far more people).
Let's assume that in the year before my birth, 1966, I am aware of 156 people who died, and in year 0 (i.e. 1 BC) I am aware of zero. That is not strictly true, as there are probably dozens of Romans, Greeks, and others whose name I would recognize, but collectively that would amount to under 1000.
So, if we do a straight-line interpolation (again I am sure this is wrong, but I don't know the exact shape of the function, and this certainly over-estimates), then I know 156 * 0.5 * 1966 people (1/2 base * height), which is 153,348 historic personages. WOW! (I should have been a great quizbowl player). We could assume a negative exponential function, and do an integral, but calculus is no fun.
I could adjust this by assuming I only know of 1000 people between 1 BC and 1000 AD, and then doing a straight line estimate from years 1000 to 1966, which would give 156 * 0.5 * 966 = 75,348. This too is likely an overestimate, but it gives me a plausible number.
OK, adding this all up
15,600 + 7,800 + 1,000 + 1,000 + 75,348 = 100748 people. So my order of magnitude upper bound of my estimate is 100,000. The real number is probably between 33,000 and 100,000.
This excludes the people I actually know, which is a mere fraction of the people I know of.
[Ernest Borgnine's best role was perhaps Marty, which we quote in Planning for Place and Plexus].