I'm not sure what you mean by "last episode you watched". I'm constantly watching Trek, on and off. And that's most likely true for most people around here.
Last TV episode was TOS "Doomsday Machine" - one of my favorites which we just got on DVD. However, I've been scrutinizing the movies so I can help my wife make our son's TWOK costume for the forthcoming Creation Star Trek con in Las Vegas.
The last episode I watched was VOY "Caretaker" Parts 1 and 2. I introduced it to my sister last night who enjoyed it and wants to continue! Yay!!
TOS: Patterns of Force. I watched because I'm currently studying for a History test and there, I will describe how are the Third Reich/SS uniforms.