Not sure if this has always been the case, but I notice that only when I log in, does the computer establish a network connection (e.g. on eth0).
Is this the standard behaviour? What if I wanted the computer to connect to the network without me logging in so I can log in remotely?
Presumably because the network manager uses user specific network settings located in that user's home folder. The global network settings go into /etc/network/interfaces, which is a common way to set up networking on CLI servers. The down side is, you'll have to stop using the network manager. Here are some examples: http://www.cyberciti.biz/faq/setting-up-an-network-interfaces-file/
mikewhatever has given the answer I needed (and answered my primary question), so to answer the secondary question ("What if I wanted the computer to connect to the network without me logging in so I can log in remotely?"), all I needed to do was add the following to /etc/network/interfaces:
and voila!