You've just gotta keep track of those units and it'll all become obvious to you:

First molarity is moles over L, so just replace all M's with mol/L, and change mL into L.  Whenever you see the word "of" in any kind of problem involving math, it means multiply.  So if you're using 25mL of 1.6M of acetic acid, you're going to multiply them together.  0.025L X 1.6mol/L... notice how the units cancel; when dealing with these equations you're never going to get a mol², L², or anything similar unless its length, and even then you're probably doing something wrong if you have to do that... so cancel cancel cancel units!

Notice how you're not going to get molarity, but moles and there's no way around it with the information you gave.

Here's just a few reminders about conversions in chemistry:

Concentration X Volume = Mass(or Moles depending on concentration convention)
Moles X Molar Mass = Mass
Mass/Molar Mass = Moles

All of the understanding lies within keeping track of the units and canceling them out; if its not canceling, just multiply by its inverse.

If you put 25 mL of 1.6 M acetic acid, then, what is the molarity of acetic acid?

Is it just 1.6 M x .025 L, or is it .160 M / .025 L?

Molarity is 1.6M.

That's another horse of color if you want to calculate  a concentration of species in this solution (H⁺, CH₃CCO^- and undissociated CH₃COOH) as Geodome suggests.

And..if you have 10 mL of 0.160 M sodium acetate , what is the moles of acetate in the solution?  

Is it .160 M X .01 L,

OK