On both my bikes, either of which I might commute with (one is officially the commuter, but the road 'fun' bike also gets ridden to work), I have: Mini pump (with a pressure gauge), spare tube, patch kit, tire levers, & a set of allen wrenches.
All are attached to the bike either under the seat, or on the frame (pump). I do carry both a spare tube and a patch kit- I have had 3 flats in a single ride before. It's part of why I prefer a mini pump over CO2- not only do you avoid the ongoing expense of buying cartridges, but you don't run out. Well, your arm might give out, but that's a different problem.