Pushbutton Ground Selection
I would have used a microcontroller with some transistors and a short code, but if you want to use logic, maybe you could go for a JK Flip-Flop with transistors on their output. 

Each button can set a pulse to both J and K on a single flip-flop, and also send a pulse to the K-input on all others. This way, when you press one button, the output of its respective flip-flop will toggle its output and change the transistor state, hence turning on/off the LED. At the same time it sends a reset to all others and turning their output (transistors) off. I am not very used to using latches, I prefer a microcontroller, so please correct me if I am wrong on this. 







simulate this circuit &ndash; Schematic created using CircuitLab