I find that, if I like a lift, it's most likely not effective. One of the signs of effectiveness in my experience is how much misery a lift can create.
As far as effective, non-powerlifting lifts go.
-Car deadlift simulator
You can pile the weight up stupid high on this lift, especially if you put the weight behind you. It requires little technique, and in turn means you can just push stupidly hard and really leave nothing behind. I liked starting with a weight I could do for 6-8 reps and working up to 15 before throwing another 45 per side and starting the process over.
-Safety squat bar squat
I am a hugely vocal proponent of the SSB, and any chance I can turn someone on to it, I try. Along with the fact you can use it to work around pretty much any limb injury (you can squat with broken hands, arms, shoulders, etc AND with a bad leg, as being able to hold the bar with one hand means you can use the other hand to brace and lower yourself down), the camber in the bar makes the squat a much more brutal exercise than normal.
The entire time you try to squat, the bar is trying to shove your face into the floor, and in turn you have to fight with all your power to keep that from happening. Along with developing a strong lower body, you develop an ugly strong upper back as well. Also, like the car deadlift simulator, it makes the squat a far more brutal than technical lift, for if the weight falls forward, you can still muscle it back up.
Upper body press
-Keg/sandbag clean and press
Once again, you can't really be talented here, you just have to be ugly strong to get it moving. It's also nice that these implements are dirt cheap.