fridge
like caliman said.......if they are fresh let them cool off at room temp then put them in the fridge. I buy La Tapatia corn tortillas(made in Turlock), i buy them in Riverbank(fresh and still warm) and i'll let them cool off and store them in the fridge. Tortillas don't have much of a 'life-span' so it's best if you use them within 3 weeks. Don't buy tortillas at your supermarket(Raley's Savemart, Albetsons etc.). Normally small mexican markets carry the locally made corn tortillas. Buy those!
btw.......how do you warm your tortillas? Do you use a comal? I use a comal(not too thick) on medium heat and place the wrinkley side of the tortillas facing each other(there's two sides to a store bought corn tortilla......the flat smooth side and the wrinkley side) You'll notice that your corn tortillas aren't as stiff as opposed to warming them individually, and they're really soft. This only applies to store bouth corn tortillas. With flour tortillas i warm them individually and get good results.
Every tortilla company makes them differently its up to you to find the right one. Also the heating techniques help your tortilla go well with whatever you're eating.