Multiplication sign in TeXForm?

Here is a very robust (!!) method

expr = (z14 z43 (z01 + z03 + z12 + z32) + z01 z12 z43 + z03 z14 z32);
StringReplace[ToString[expr, TeXForm], " " :> "\\times"]

Using Ctrl+Shift+C to copy as plain text results in

$$\text{z14}\times\text{z43}\times(\text{z01}+\text{z03}+\text{z12}+\text{z32})+\text{z01}\times\text{z12}\times\text{z43}+\text{z03}\times\text{z14}\times\text{z32}$$

Edit

The above approach might serve you well in the simple setting the OP is representing, in general, this method is very likely to break, because it relies on that a multiplication is converted into a single space in TeXForm.

As questions in our latex tag suggest, there are several problems and subtilities with TeXForm and a general and always working answer can hardly be given at this point without further information.

We want cross? Let's use Cross!

expr /. Times -> Cross // TeXForm

$ \text{z14}\times (\text{z01}+\text{z03}+\text{z12}+\text{z32})\times \text{z43}+\text{z01}\times \text{z12}\times \text{z43}+\text{z03}\times \text{z14}\times \text{z32} $

Row appears to work:

expr = (z03*z14*z32 + z01*z12*z43 + z14*(z01 + z03 + z12 + z32)*z43);
expr /. Times :> (Row[{##}, "\[Times]"] &) // TeXForm

Copying as plain text as halirutan did and wrapping in $ symbols:

$\text{z14}\times \text{z01}+\text{z03}+\text{z12}+\text{z32}\times \text{z43}+\text{z01}\times \text{z12}\times \text{z43}+\text{z03}\times \text{z14}\times \text{z32}$

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• Note: This code fails in recent versions due to a bug: Incompatibility of Row and TeXForm.
  kguler discovered that the bug may be circumvented by setting:

  BoxForm`$UseTemplateSlotSequenceForRow = False;