74ls139--are they supposed to do this?
Many beginners are confused by the fact that bipolar TTL (plain 74xx, 74LS, 74ALS and others) inputs source current, and will act as logic High with no connection.  To get a logic Low input, you must connect the input to directly to ground, or to ground with a low resistance - under 500 Ohms should work.

CMOS parts (74C, 74HC, or anything with a "C" in the middle) will have a very high input impedance, and may float randomly between High and Low if left unconnected.  Fairly high value (5 - 10K Ohm) pull-up or pull-down resistors can be used to force otherwise-unused inputs to a known state.