My bud has a 16ohm cabinet he wants to pop some new speakers in, do I order 16ohm speakers or 8ohm?
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Why not just look at the ratings on the speakers he'll be taking out of that cab? The speakers have the rating clearly printed on the label on the bottom end of the magnet on the speaker.
It depends how the speakers are wired.

If you wire two 8 ohm speakers in series, you'd have 16 ohm total for the cab. (assuming you are dealing with 2 speakers)

Without more info (ie, what size cab, etc) I can't really give any specific advice. But if you wish to avoid the hassle of "thinking" about this, do what the above user noted; note the impedance of the speakers currently there and buy new ones of the same impedance, and simply put in the new speakers (with the same wiring setup).