To what is bitcoind memory usage bound? I am interested in running a well-connected node, and I was wondering: is the memory footprint directly correlated to the number of connections?

And more broadly: with what RAM usage increases?
RAM usage increases until it is slightly less than the total RAM available. This is due to the design of the operating system which intentionally keeps as little RAM free as possible, using all excess RAM as a disk cache to reduce I/O.