I'm playing Payday for steam's free weekend, and notice that I can take civilians hostage. Other than preventing them from getting up and getting shot, is there any point to doing so?
The hostages system gives you the opportunity to free one of your teamates from jail. Since you can't really "die" in Payday, this is their "revival" system.
You can take civilians as hostages (just by shouting at them and handcuffing them) or even cops. Taking cops as hostages is a bit more tricky: you must hit them first (with a non-lethal shoot or with your melee attack) and then shout at them until they handcuff themselves (which will save you a pair of handcuffs).
If one of your teammates gets arrested, you'll have to wait the end of the assault plus the eventual time malus (if they killed civilians) to proceed to the trade.
Be careful with your hostages, because you cannot make them move. So if you leave them without surveilance, they can be freed by the cops.
If one of the players gets arrested (aka killed), Bain (the guy who gives your orders) will start negotiating with the police.
After a while (depending on how many civilians were killed), a hostage is selected and if you free him/her, the arrested player respawns.