A serpentine should not be taut completely tight to the point of no movement. Also, it should not be too loose to the point of sloppy play in the belt on the idler pulley. You may find specifications published in a repair manual for your vehicle that you can find at your local auto parts store.
Are you replacing your belt, OR are you having a sound that you are trying to correct? Check your owners manual for specifications, you may need a service manual to find this.
That being said, a loose or over tight belt will cause noise but your car should have an automatic belt tensioner that automatically adjusts the belt as needed. If you are replacing a bad belt, and there is still a problem, there could be a pulley that is starting to go bad. On average you should have about 1/4 to 1/2" of slack on a belt, any more than 1/2 = too loose, anything less than 1/4 = too tight.
I hope that helps.
〉 Answered on Apr 20th, 2010 by Audra Fordin, Owner at Great Bear Auto Shop