So much has been made in the last few weeks of the "50+ base weapons" quote from Mr. Howard. One of the recurrent reactions seems to be "oh come on, Fallout 3 had 137 weapons/219 weapons/tons and tons of weapons." The exact number seems to vary drastically based on what criteria people choose to use when counting them all up.
I decided to see if I could cut through all the wild assertions and figure out how exactly the "50+ base weapons" deal stacks up to the previous entry. The criteria I used when counting is what I imagine the devs use when considering how many weapons the need to make; namely, "How many uniquely shaped weapons are there?" the same gun with a different texture, gun sound, etc., does not count as a unique weapon. Thus, while a plasma pistol and a plasma rifle are two unique weapons, the scoped .44 magnum and the Blackhawk are not.
With this in mind I counted sixty-six different weapons; keep in mind this INCLUDES all unique DLC weapons. This number seems pretty closely in line with the number in Fallout 4, without the insanely cool looking mod system that should add a huge amount of variety to the game.
TL;DR: Chill people. There are bound to be plenty of weapons for everyone.