: Halo 1, 2, and 3 all have levels where Master Chief needs to rescue captured
: marines from Covenant prisons. But if the overall goal of the Covenant is
: to exterminate the human race, why in the world do they take any prisoners
: in the first place?

In Halo CE, I believe that Captain Keyes and other soldiers were taken for information. Particularly, the Elites were interested in finding out how the Pillar of Autumn had found Alpha Halo, and the troopers were abducted to be tortured in front of Keyes to break him. I wouldn't be surprised if the Covenant often did this when they found a high-ranking officer.

"Und now, miserable vermin, you will tell us of the fleet movements, wort?"

In Halo 2, we saw Miranda Keyes taken prisoner, and Marines were held in High Charity. I believe that the rational behind their captivity was one and the same: the Heirarchs knew that a Human was absolutely essential to the activation of the Halo array.

In Halo 3, Johnson was initially captured because... to draw the Chief into a fight? Sport for the Brutes? And yeah, he was captured to activate the Halo array.

In Halo Wars... Sigh. Anders was kidnapped because Regret couldn't be asked to do more than type "Password" into the terminal.

Now, other reasons why the Covenant might take prisoners? Field rations, boredom, revenge for Human counterattacks, etc. Perhaps some zealous Elites take prisoners to torture confessions of destruction of Forerunner relics out of Humans.

What I can't see as a common motive is the desire to use Humans to activate Forerunner relics. I doubt that knowledge of Human proficiency with those relics is common knowledge outside of the Heirarchs. Those that say otherwise would be branded as heretics, with 'proof' presented that Humans get those relics working much the same way that the Prophets do, only slower and messier.

And as a reminder, nineteen minutes.