That depends. At a minimum, spare tube, tire levers, and inflation device (mini pump or CO2 cannisters and inflator), seat bag to hold your spare tube, water bottle and bottle cage, floor pump, for pumping tires up at home, lock (if you plan to leave the bike unattended).

Other accessories you might find yourself wanting are short or long finger cycling gloves, computer, rack (to transport your bike), lights, riding shorts, jersey, windbreaker, shoes, clipless pedals, eye protection. You might already have some of this stuff. If you don't ride at night, you won't need lights. And maybe you already have a van or pickup truck and hence, don't absolutely need a rack to transport your bike. And maybe instead of a jersey, you might just bet by with a technical shirt or light jacket that isn't cycling specific. And, plenty of people get by with sandles, hiking shoes or running shoes and flat pedals instead of cycling shoes and clipless pedals.