Aleene's Tacky Glue, as colmmoo mentioned. It comes in a gold tube and can readily be found in craft stores. Reasonably priced, too. Craft stores also sell special glue just for foam, but I don't know if it's any better than tacky glue.
I like contact cement. Some of the glues mentioned above are basically contact cement, like the 3m spray glue (if it's the same as what I have), but more expensive. Granted spray and tube applied glues are cleaner and easer to apply, but they are more expensive.
If you're doing a professional haunt, the liquid nails and loctite may be the way to go if you're worried about high traffic areas where a piece will get bumped, grabbed or pulled on, but contact cement would probably work as well there. For the home haunt it's much more affordable.
If you do use contact cement, read the directions. You need to coat both pieces and let them dry (10-15 min?) before joining them. If you put the pieces together when the glue is still wet, the joint won't hold well.
You do have to be careful in applying it to avoid a mess; you basically can't wipe it off most surfaces once it's on there, and you only have limited repositioning possibilities. But I'm a cheap old buzzard and don't mind taking the extra care.
I've used contact cement to mount foam in my kayak and it holds up well to vibration and wear, even in repeated class III-V whitewater (an old hobby of mine).
I use the Liquid Nails Construction Adhesive. (It comes in a gold colored tube.)
It doesn't say on the tube that it works on styrofoam, but believe me it does. It won't eat the styrofoam or foam board and it dries FAST!!