We have (or will have soon) 3 production servers and 1 dev server, with approximately 150 databases across them all. I am the de facto DBA, although we do not have that actual position/title at present (my official title is Applications Programmer Analyst).
I have been, over the past several months, working on automating as much as possible, due to the simple fact that administering databases and servers is not my primary job. Backups, index maintenance, integrity checking, monitoring... I have been working to implement as much automation as possible. The hardest part is not knowing what I don't know; I know there are things that I should be looking at, but I have not had much time to dive into those areas, and the time usually comes when an issue appears (funny how priorities can change rather quickly in emergencies...). If it weren't for the level of automation, I know from experience that there are things that just wouldn't be done.