I don't recall exactly, but probably 1-4GB. Not particularly low memory, but when something would come along that needed more memory than the system had, say a load burst, I was quite surprised to find the systems without swap just stop responding. I was expecting OOM killer to kill the offending process, the load balancer to remove it from the load, monitoring to say what process had gotten killed, but instead, even after waiting half an hour, the system was just wedged.

That seems pretty low, especially if this was 1GB of RAM. I'd use swap on such systems. I don't think there are any reasons today to buy physical machines with that little RAM, but I can see how you might have such VMs,

That said, I agree with other commenters that said this sounds like a kernel bug. I am wondering what was going on to wedge the system that bad. Would putting executables on tmpfs (so they cannot be paged out) helped?