@alexhall it really depends. You can get with much simpler stacks. I am still using Nagios and it brings me what I need in about 90mb of RAM.
(Not that I would recommend it in general.)
Graphs and distributed logs are very nice, but you often don't need them. All the old monitoring software still works.
You mentioned log monitoring. I was using Graylog some time ago and it was quite nice and simple too.