I oil the chain about once a week, and clean it about once a month. (It's needing it right now.)
Top off the tires just before each ride because I notice a real difference between fully-pumped tires and slightly soft ones.

Unless something breaks, so far, that's it.

I have a loose fender that I aim to properly secure in the next week or so, but that's because I never completely finished its original installation 9 months ago.