With modern machinery that's well maintained you can generally rely upon driver warning systems to alert you to possible issues. But I still walk round the car every few days and look for possible problems.
I'm close to neurotic about having cars that drive correctly and I still do the stationary and moving brake tests when starting any journey, no matter how short.
Stationary for pedal feel. On the move as soon as possible I do a moving brake test.
I also check tyre pressures even fortnight or so. But I'm such a fussy driver that I'd spot an underinflated tyre pretty quickly anyway.
I like to have a full screen wash tank but again most cars will tell you that it's running low.
Strangely I never check engine oil level regularly and rely upon warning systems to tell me that it needs attention.