Excel Formula: If Cell B equals X then copy Cell C

You wan to COPY the data or you just want the value to show in that cell?  Copying a cell is a VBA thing which is a bit more involved.  If you just want to show the value used this:

=IF(OR(B15="x",B15="X"),C15,"")
If B15 is x or X then show the value in this cell, else show empty

Actually Excel is not case sensitive so this would work too.

=IF(B15="x",C15,"")

Good simple answer.

What if I want to copy a string of outputs with commas in between but drop the comma if the first cell is blank

Eg If A2=x, to return the Initials in A1, and keep going across columns but to drop the relevant column if Row 2 is blank

There and easy way (less elegant) and a harder way.

Easy, create a hidden row in row 3 (for this example) and use this formula:
In A3 cell:
=IF(A2="x",A1,"")


EDITED (Original was wrong)
In B2
=IF(B2="x",A3&", "&B1,A3)

Then copy and base B2 cell across all the column.  If you have Z column the last cell Z3 should have all your data.

As for the hard way I would think of using matrix but I need to dig a bit for that one.  

Let me know if what I mentioned here is enough.  If not I'll look into matrix's.

I did not test this... if it does not work let me know and I'll debug it for you.

I think I follow but I need it to string a series of columns ideally with a comma when there is an initial, and to leave out the space and comma when there is no initial

Whereas the formula you've used will still give me a space between commas where there is no initial?
 
AB      CD            AD      CC
x            x            x
AB      AB      AB,       AB,       AB, , CC

It shouldn't I just tested it.

I attached an excel file with the formula.

AB      CD      AD      CC      DE      FE      YT
x            x            x            x
AB      AB      AB, AD      AB, AD      AB, AD, DE      AB, AD, DE      AB, AD, DE, YT
example.xls