How many chem addictions are in Fallout 4?

The 'mixed' chems addicts you to their prefix. For example, Buffjet addicts you to Buffout and Psychobuff addicts you to Psycho.

Special chems which does not contain the name of another chem have their own addiction. For example, X-Cell or Overdrive have their own addiction, even if the latter is made with Psycho. By the same rule, Berry Mentats or Ultra Jet addicts you to Mentats and Jet respectively.

You can also get addicted to alcohol (Any type), which is in its own category.

I was able to get addicted to a total of 11 different things.

Here's the effect of all the addictions on a character:

As you can see, he's suffering a total loss of 26 SPECIAL points and 20 damage resist. Don't do drugs kids.

If paired with the Junkie legendary mod, on a simple 110 damage unmodded Gauss Rifle, you can get a nice 265% damage boost:

It seems to stay consistent between different weapon types, a standard 10mm pistol with no upgrades will go from 18 to 47 damage.

Do drugs kids.