Why do some people who are not related by blood look alike?

A simple google image search for ‘similar looking people’

We all are related. Genetically. We all belong to the same gene pool.

Everybody on earth is at least 50th cousin with everybody else on the earth. Biologically, it is not so difficult to be almost identical.

If you go back just 65 generations (the time when Rome empire what building), you will require at least 1,000,000,000,000,000,000 people (I mean your parents, their parents, their parents, etc.) in all. This number is larger that the total number of human ever to be present on this planet. In fact larger that the total number of all of monkeys and primates together. This makes no sense. The only valid inference for this is that our ancestor were mostly practicing incest.

The further back in time you go, the lesser is the number of people. This suggests that there was a lot of incest. In fact there is a 1 in 5 chance that your neighbor(or your wife/date) and you were are from same family fewer than 10 generations ago.

There is no surprise as to why so many people look alike. In fact the picture you have posted are of famous people. There are other too. Lot of them. You may also be interested in the study that says everybody has a twin somewhere on this planet. 
They do say EVERYBODY has a twin: Mind-boggling portraits of unrelated look-alikes

Also, if you might observe, most of mentally disabled people look amazingly alike!!!

The following thread from Reddit makes sense.

When a sperm and egg come together and it grows into a baby, there are a million things that can go wrong. It’s really common to have an extra chromosome, or a missing chromosome, or a large piece of one that’s missing or upside-down.Most of the time, these mutations lead to death (miscarriage) of the fetus.Only a tiny number of mutations to your genetic code actually allow the fetus to survive. So those are the ones who are born, and what we observe is that babies who have something wrong with them typically have one of a set of common genetic abnormalities. It’s not that those are the only possible abnormalities — it’s that all of the other abnormalities are too severe.