It always depends on several factors, including how much of a trade relationship runs between the two, or regional defence agreements (among other things).
And while IANAL, I suspect given the relationships we have, the Bahamas almost certainly would, Turkey would be contingent, and Spain would likely be the most resistant for non-economic (capital crimes) as EU states tend to be, but for economic ones...almost certainly extradite someone back to US remand (as has happened before).
